Smallest transitive degree

When G acts on a (finite) set, the set is a disjoint union of orbits, the transitive G-sets. There is a natural bijection

{transitive G-sets up to ≅}	↔	{subgroups of G up to conjugacy}
X	↦	stabiliser of a point
G/H	↤	H

Transitive G-sets on which G acts faithfully correspond to subgroups H with trivial core (or core-free), that is those where the intersection of H with all of its conjugates is trivial; equivalently, H contains no non-trivial normal subgroup of G. In this case G can be viewed as a transitive subgroup of S_n for n=(G:H), the index of H in G, called the transitive degree. Conversely, all transitive subgroups of S_n arise in this way. The transitive group database in GAP and Magma contains all transitive subgroups of S_n up to conjugacy for n≤31, numbered nTi (or T_n,i).

See all transitive groups of degree up to 15 and up to 31 for the transitive group numbering. The table below orders groups by the smallest n for which G is a transitive subgroup of S_n, provided n≤120. In other words, it is the index of the largest core-free subgroup H of G. (Often H={1}, for example for abelian and many other soluble groups, so G may only act transitively on itself by left multiplication, by the regular action.)

On 1 point

Groups of order 1

		d	ρ	Label	ID
C₁	Trivial group	1	1+	C1	1,1

On 2 points

Groups of order 2

		d	ρ	Label	ID
C₂	Cyclic group	2	1+	C2	2,1

On 3 points

Groups of order 3

		d	ρ	Label	ID
C₃	Cyclic group; = A₃ = triangle rotations	3	1	C3	3,1

Groups of order 6

		d	ρ	Label	ID
S₃	Symmetric group on 3 letters; = D₃ = GL₂(𝔽₂) = triangle symmetries = 1^st non-abelian group	3	2+	S3	6,1

On 4 points

Groups of order 4

		d	ρ	Label	ID
C₄	Cyclic group; = square rotations	4	1	C4	4,1
C₂²	Klein 4-group V₄ = elementary abelian group of type [2,2]; = rectangle symmetries	4		C2^2	4,2

Groups of order 8

		d	ρ	Label	ID
D₄	Dihedral group; = He₂ = AΣL₁(𝔽₄) = 2₊¹⁺² = square symmetries	4	2+	D4	8,3

Groups of order 12

		d	ρ	Label	ID
A₄	Alternating group on 4 letters; = PSL₂(𝔽₃) = L₂(3) = tetrahedron rotations	4	3+	A4	12,3

Groups of order 24

		d	ρ	Label	ID
S₄	Symmetric group on 4 letters; = PGL₂(𝔽₃) = Aut(Q₈) = Hol(C₂²) = tetrahedron symmetries = cube/octahedron rotations	4	3+	S4	24,12

On 5 points

Groups of order 5

		d	ρ	Label	ID
C₅	Cyclic group; = pentagon rotations	5	1	C5	5,1

Groups of order 10

		d	ρ	Label	ID
D₅	Dihedral group; = pentagon symmetries	5	2+	D5	10,1

Groups of order 20

		d	ρ	Label	ID
F₅	Frobenius group; = C₅ ⋊C₄ = AGL₁(𝔽₅) = Aut(D₅) = Hol(C₅) = Sz(2)	5	4+	F5	20,3

Groups of order 60

		d	ρ	Label	ID
A₅	Alternating group on 5 letters; = SL₂(𝔽₄) = L₂(5) = L₂(4) = icosahedron/dodecahedron rotations; 1^st non-abelian simple	5	3+	A5	60,5

Groups of order 120

		d	ρ	Label	ID
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	5	4+	S5	120,34

On 6 points

Groups of order 6

		d	ρ	Label	ID
C₆	Cyclic group; = hexagon rotations	6	1	C6	6,2

Groups of order 12

		d	ρ	Label	ID
D₆	Dihedral group; = C₂×S₃ = hexagon symmetries	6	2+	D6	12,4

Groups of order 18

		d	ρ	Label	ID
C₃×S₃	Direct product of C₃ and S₃; = U₂(𝔽₂)	6	2	C3xS3	18,3

Groups of order 24

		d	ρ	Label	ID
C₂×A₄	Direct product of C₂ and A₄; = AΣL₁(𝔽₈)	6	3+	C2xA4	24,13

Groups of order 36

		d	ρ	Label	ID
C₃²⋊C₄	The semidirect product of C₃² and C₄ acting faithfully	6	4+	C3^2:C4	36,9
S₃²	Direct product of S₃ and S₃; = Spin+₄(𝔽₂) = Hol(S₃)	6	4+	S3^2	36,10

Groups of order 48

		d	ρ	Label	ID
C₂×S₄	Direct product of C₂ and S₄; = O₃(𝔽₃) = cube/octahedron symmetries	6	3+	C2xS4	48,48

Groups of order 72

		d	ρ	Label	ID
S₃≀C₂	Wreath product of S₃ by C₂; = SO+₄(𝔽₂)	6	4+	S3wrC2	72,40

Groups of order 360

		d	ρ	Label	ID
A₆	Alternating group on 6 letters; = PSL₂(𝔽₉) = L₂(9); 3^rd non-abelian simple	6	5+	A6	360,118

On 7 points

Groups of order 7

		d	ρ	Label	ID
C₇	Cyclic group	7	1	C7	7,1

Groups of order 14

		d	ρ	Label	ID
D₇	Dihedral group	7	2+	D7	14,1

Groups of order 21

		d	ρ	Label	ID
C₇⋊C₃	The semidirect product of C₇ and C₃ acting faithfully	7	3	C7:C3	21,1

Groups of order 42

		d	ρ	Label	ID
F₇	Frobenius group; = C₇ ⋊C₆ = AGL₁(𝔽₇) = Aut(D₇) = Hol(C₇)	7	6+	F7	42,1

Groups of order 168

		d	ρ	Label	ID
GL₃(𝔽₂)	General linear group on 𝔽₂³; = Aut(C₂³) = L₃(2) = L₂(7); 2^nd non-abelian simple	7	3	GL(3,2)	168,42

On 8 points

Groups of order 8

		d	ρ	Label	ID
C₈	Cyclic group	8	1	C8	8,1
C₂×C₄	Abelian group of type [2,4]	8		C2xC4	8,2
Q₈	Quaternion group; = C₄ .C₂ = Dic₂ = 2_-¹⁺²	8	2-	Q8	8,4
C₂³	Elementary abelian group of type [2,2,2]	8		C2^3	8,5

Groups of order 16

		d	ρ	Label	ID
C₂²⋊C₄	The semidirect product of C₂² and C₄ acting via C₄/C₂=C₂	8		C2^2:C4	16,3
M₄(2)	Modular maximal-cyclic group; = C₈ ⋊₃ C₂	8	2	M4(2)	16,6
D₈	Dihedral group	8	2+	D8	16,7
SD₁₆	Semidihedral group; = Q₈ ⋊C₂ = QD₁₆	8	2	SD16	16,8
C₂×D₄	Direct product of C₂ and D₄	8		C2xD4	16,11
C₄○D₄	Pauli group = central product of C₄ and D₄	8	2	C4oD4	16,13

Groups of order 24

		d	ρ	Label	ID
SL₂(𝔽₃)	Special linear group on 𝔽₃²; = Q₈ ⋊C₃ = 2T = <2,3,3> = 1^st non-monomial group	8	2-	SL(2,3)	24,3

Groups of order 32

		d	ρ	Label	ID
C₂³⋊C₄	The semidirect product of C₂³ and C₄ acting faithfully	8	4+	C2^3:C4	32,6
C₄.D₄	1^st non-split extension by C₄ of D₄ acting via D₄/C₂²=C₂	8	4+	C4.D4	32,7
C₄≀C₂	Wreath product of C₄ by C₂	8	2	C4wrC2	32,11
C₂²≀C₂	Wreath product of C₂² by C₂	8		C2^2wrC2	32,27
C₈⋊C₂²	The semidirect product of C₈ and C₂² acting faithfully; = Aut(D₈) = Hol(C₈)	8	4+	C8:C2^2	32,43
2₊¹⁺⁴	Extraspecial group; = D₄ ○D₄	8	4+	ES+(2,2)	32,49

Groups of order 48

		d	ρ	Label	ID
GL₂(𝔽₃)	General linear group on 𝔽₃²; = Q₈ ⋊S₃ = Aut(C₃²)	8	2	GL(2,3)	48,29

Groups of order 56

		d	ρ	Label	ID
F₈	Frobenius group; = C₂³ ⋊C₇ = AGL₁(𝔽₈)	8	7+	F8	56,11

Groups of order 64

		d	ρ	Label	ID
C₂≀C₄	Wreath product of C₂ by C₄; = AΣL₁(𝔽₁₆)	8	4+	C2wrC4	64,32
C₄²⋊C₄	2^nd semidirect product of C₄² and C₄ acting faithfully	8	4+	C4^2:C4	64,34
D₄⋊₄D₄	3^rd semidirect product of D₄ and D₄ acting via D₄/C₂²=C₂; = Hol(D₄)	8	4+	D4:4D4	64,134
C₂≀C₂²	Wreath product of C₂ by C₂²; = Hol(C₂×C₄)	8	4+	C2wrC2^2	64,138

Groups of order 96

		d	ρ	Label	ID
C₂⁴⋊C₆	1^st semidirect product of C₂⁴ and C₆ acting faithfully	8	6+	C2^4:C6	96,70
C₂³⋊A₄	2^nd semidirect product of C₂³ and A₄ acting faithfully	8	4+	C2^3:A4	96,204
C₂²⋊S₄	The semidirect product of C₂² and S₄ acting via S₄/C₂²=S₃	8	6+	C2^2:S4	96,227

Groups of order 128

		d	ρ	Label	ID
D₄≀C₂	Wreath product of D₄ by C₂	8	4+	D4wrC2	128,928

Groups of order 168

		d	ρ	Label	ID
AΓL₁(𝔽₈)	Affine semilinear group on 𝔽₈¹; = F₈ ⋊C₃ = Aut(F₈)	8	7+	AGammaL(1,8)	168,43

Groups of order 192

		d	ρ	Label	ID
C₂≀A₄	Wreath product of C₂ by A₄	8	4+	C2wrA4	192,201
C₂⁴⋊D₆	1^st semidirect product of C₂⁴ and D₆ acting faithfully; = Aut(C₂×Q₈)	8	6+	C2^4:D6	192,955
C₂³⋊S₄	2^nd semidirect product of C₂³ and S₄ acting faithfully; = Aut(C₂²×C₄)	8	4+	C2^3:S4	192,1493
Q₈⋊₂S₄	2^nd semidirect product of Q₈ and S₄ acting via S₄/C₂²=S₃; = Hol(Q₈)	8	4+	Q8:2S4	192,1494

Groups of order 288

		d	ρ	Label	ID
A₄≀C₂	Wreath product of A₄ by C₂	8	6+	A4wrC2	288,1025

Groups of order 336

		d	ρ	Label	ID
PGL₂(𝔽₇)	Projective linear group on 𝔽₇²; = GL₃(𝔽₂)⋊C₂ = Aut(GL₃(𝔽₂)); almost simple	8	6+	PGL(2,7)	336,208

On 9 points

Groups of order 9

		d	ρ	Label	ID
C₉	Cyclic group	9	1	C9	9,1
C₃²	Elementary abelian group of type [3,3]	9		C3^2	9,2

Groups of order 18

		d	ρ	Label	ID
D₉	Dihedral group	9	2+	D9	18,1
C₃⋊S₃	The semidirect product of C₃ and S₃ acting via S₃/C₃=C₂	9		C3:S3	18,4

Groups of order 27

		d	ρ	Label	ID
He₃	Heisenberg group; = C₃² ⋊C₃ = 3₊¹⁺²	9	3	He3	27,3
3_-¹⁺²	Extraspecial group	9	3	ES-(3,1)	27,4

Groups of order 54

		d	ρ	Label	ID
C₃²⋊C₆	The semidirect product of C₃² and C₆ acting faithfully	9	6+	C3^2:C6	54,5
C₉⋊C₆	The semidirect product of C₉ and C₆ acting faithfully; = Aut(D₉) = Hol(C₉)	9	6+	C9:C6	54,6
He₃⋊C₂	2^nd semidirect product of He₃ and C₂ acting faithfully; = Aut(3_-¹⁺²)	9	3	He3:C2	54,8

Groups of order 72

		d	ρ	Label	ID
F₉	Frobenius group; = C₃² ⋊C₈ = AGL₁(𝔽₉)	9	8+	F9	72,39
PSU₃(𝔽₂)	Projective special unitary group on 𝔽₂³; = C₃² ⋊Q₈ = M₉	9	8+	PSU(3,2)	72,41

Groups of order 81

		d	ρ	Label	ID
C₃≀C₃	Wreath product of C₃ by C₃; = AΣL₁(𝔽₂₇)	9	3	C3wrC3	81,7

Groups of order 108

		d	ρ	Label	ID
C₃²⋊D₆	The semidirect product of C₃² and D₆ acting faithfully	9	6+	C3^2:D6	108,17

Groups of order 144

		d	ρ	Label	ID
AΓL₁(𝔽₉)	Affine semilinear group on 𝔽₉¹; = F₉ ⋊C₂ = Aut(C₃²⋊C₄)	9	8+	AGammaL(1,9)	144,182

Groups of order 162

		d	ρ	Label	ID
C₃≀S₃	Wreath product of C₃ by S₃	9	3	C3wrS3	162,10
C₃³⋊C₆	1^st semidirect product of C₃³ and C₆ acting faithfully	9	6+	C3^3:C6	162,11
C₃³⋊S₃	2^nd semidirect product of C₃³ and S₃ acting faithfully	9	6+	C3^3:S3	162,19

Groups of order 216

		d	ρ	Label	ID
ASL₂(𝔽₃)	Hessian group = Affine special linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊C₃	9	8+	ASL(2,3)	216,153

Groups of order 324

		d	ρ	Label	ID
He₃⋊D₆	The semidirect product of He₃ and D₆ acting faithfully	9	6+	He3:D6	324,39
C₃³⋊A₄	The semidirect product of C₃³ and A₄ acting faithfully	9	4	C3^3:A4	324,160

Groups of order 432

		d	ρ	Label	ID
AGL₂(𝔽₃)	Affine linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊S₃ = Aut(C₃⋊S₃) = Hol(C₃²)	9	8+	AGL(2,3)	432,734

On 10 points

Groups of order 10

		d	ρ	Label	ID
C₁₀	Cyclic group	10	1	C10	10,2

Groups of order 20

		d	ρ	Label	ID
D₁₀	Dihedral group; = C₂×D₅	10	2+	D10	20,4

Groups of order 40

		d	ρ	Label	ID
C₂×F₅	Direct product of C₂ and F₅; = Aut(D₁₀) = Hol(C₁₀)	10	4+	C2xF5	40,12

Groups of order 50

		d	ρ	Label	ID
C₅×D₅	Direct product of C₅ and D₅; = AΣL₁(𝔽₂₅)	10	2	C5xD5	50,3

Groups of order 80

		d	ρ	Label	ID
C₂⁴⋊C₅	The semidirect product of C₂⁴ and C₅ acting faithfully	10	5+	C2^4:C5	80,49

Groups of order 100

		d	ρ	Label	ID
C₅²⋊C₄	4^th semidirect product of C₅² and C₄ acting faithfully	10	4+	C5^2:C4	100,12
D₅²	Direct product of D₅ and D₅	10	4+	D5^2	100,13

Groups of order 120

		d	ρ	Label	ID
C₂×A₅	Direct product of C₂ and A₅; = icosahedron/dodecahedron symmetries	10	3+	C2xA5	120,35

Groups of order 160

		d	ρ	Label	ID
C₂⁴⋊D₅	The semidirect product of C₂⁴ and D₅ acting faithfully	10	5+	C2^4:D5	160,234
C₂×C₂⁴⋊C₅	Direct product of C₂ and C₂⁴⋊C₅; = AΣL₁(𝔽₃₂)	10	5+	C2xC2^4:C5	160,235

Groups of order 200

		d	ρ	Label	ID
C₅²⋊C₈	The semidirect product of C₅² and C₈ acting faithfully	10	8+	C5^2:C8	200,40
D₅⋊F₅	The semidirect product of D₅ and F₅ acting via F₅/D₅=C₂; = Hol(D₅)	10	8+	D5:F5	200,42
D₅≀C₂	Wreath product of D₅ by C₂	10	4+	D5wrC2	200,43
C₅²⋊Q₈	The semidirect product of C₅² and Q₈ acting faithfully	10	8+	C5^2:Q8	200,44

Groups of order 240

		d	ρ	Label	ID
C₂×S₅	Direct product of C₂ and S₅; = O₃(𝔽₅)	10	4+	C2xS5	240,189

Groups of order 320

		d	ρ	Label	ID
C₂⁴⋊F₅	The semidirect product of C₂⁴ and F₅ acting faithfully	10	5+	C2^4:F5	320,1635
C₂×C₂⁴⋊D₅	Direct product of C₂ and C₂⁴⋊D₅	10	5+	C2xC2^4:D5	320,1636

Groups of order 400

		d	ρ	Label	ID
C₅²⋊M₄(2)	The semidirect product of C₅² and M₄(2) acting faithfully	10	8+	C5^2:M4(2)	400,206
D₅≀C₂⋊C₂	The semidirect product of D₅≀C₂ and C₂ acting faithfully	10	8+	D5wrC2:C2	400,207

On 11 points

Groups of order 11

		d	ρ	Label	ID
C₁₁	Cyclic group	11	1	C11	11,1

Groups of order 22

		d	ρ	Label	ID
D₁₁	Dihedral group	11	2+	D11	22,1

Groups of order 55

		d	ρ	Label	ID
C₁₁⋊C₅	The semidirect product of C₁₁ and C₅ acting faithfully	11	5	C11:C5	55,1

Groups of order 110

		d	ρ	Label	ID
F₁₁	Frobenius group; = C₁₁ ⋊C₁₀ = AGL₁(𝔽₁₁) = Aut(D₁₁) = Hol(C₁₁)	11	10+	F11	110,1

On 12 points

Groups of order 12

		d	ρ	Label	ID
Dic₃	Dicyclic group; = C₃ ⋊C₄	12	2-	Dic3	12,1
C₁₂	Cyclic group	12	1	C12	12,2
C₂×C₆	Abelian group of type [2,6]	12		C2xC6	12,5

Groups of order 24

		d	ρ	Label	ID
C₄×S₃	Direct product of C₄ and S₃	12	2	C4xS3	24,5
D₁₂	Dihedral group	12	2+	D12	24,6
C₃⋊D₄	The semidirect product of C₃ and D₄ acting via D₄/C₂²=C₂	12	2	C3:D4	24,8
C₃×D₄	Direct product of C₃ and D₄	12	2	C3xD4	24,10
C₂²×S₃	Direct product of C₂² and S₃	12		C2^2xS3	24,14

Groups of order 36

		d	ρ	Label	ID
C₃×Dic₃	Direct product of C₃ and Dic₃	12	2	C3xDic3	36,6
C₃×A₄	Direct product of C₃ and A₄	12	3	C3xA4	36,11
S₃×C₆	Direct product of C₆ and S₃	12	2	S3xC6	36,12

Groups of order 48

		d	ρ	Label	ID
C₄²⋊C₃	The semidirect product of C₄² and C₃ acting faithfully	12	3	C4^2:C3	48,3
A₄⋊C₄	The semidirect product of A₄ and C₄ acting via C₄/C₂=C₂; = SL₂(ℤ/4ℤ)	12	3	A4:C4	48,30
C₄×A₄	Direct product of C₄ and A₄	12	3	C4xA4	48,31
S₃×D₄	Direct product of S₃ and D₄; = Aut(D₁₂) = Hol(C₁₂)	12	4+	S3xD4	48,38
C₂²×A₄	Direct product of C₂² and A₄	12		C2^2xA4	48,49
C₂²⋊A₄	The semidirect product of C₂² and A₄ acting via A₄/C₂²=C₃	12		C2^2:A4	48,50

Groups of order 72

		d	ρ	Label	ID
C₆.D₆	2^nd non-split extension by C₆ of D₆ acting via D₆/S₃=C₂	12	4+	C6.D6	72,21
C₃⋊D₁₂	The semidirect product of C₃ and D₁₂ acting via D₁₂/D₆=C₂	12	4+	C3:D12	72,23
C₃×C₃⋊D₄	Direct product of C₃ and C₃⋊D₄	12	2	C3xC3:D4	72,30
C₃×S₄	Direct product of C₃ and S₄	12	3	C3xS4	72,42
C₃⋊S₄	The semidirect product of C₃ and S₄ acting via S₄/A₄=C₂	12	6+	C3:S4	72,43
S₃×A₄	Direct product of S₃ and A₄	12	6+	S3xA4	72,44
C₂×C₃²⋊C₄	Direct product of C₂ and C₃²⋊C₄	12	4+	C2xC3^2:C4	72,45
C₂×S₃²	Direct product of C₂, S₃ and S₃	12	4+	C2xS3^2	72,46

Groups of order 96

		d	ρ	Label	ID
C₂³.₃A₄	1^st non-split extension by C₂³ of A₄ acting via A₄/C₂²=C₃	12	6+	C2^3.3A4	96,3
C₄²⋊S₃	The semidirect product of C₄² and S₃ acting faithfully	12	3	C4^2:S3	96,64
C₂×C₄²⋊C₃	Direct product of C₂ and C₄²⋊C₃	12	3	C2xC4^2:C3	96,68
C₂³.A₄	2^nd non-split extension by C₂³ of A₄ acting faithfully	12	6+	C2^3.A4	96,72
C₄×S₄	Direct product of C₄ and S₄	12	3	C4xS4	96,186
C₄⋊S₄	The semidirect product of C₄ and S₄ acting via S₄/A₄=C₂	12	6+	C4:S4	96,187
A₄⋊D₄	The semidirect product of A₄ and D₄ acting via D₄/C₂²=C₂; = Aut(C₄²) = GL₂(ℤ/4ℤ)	12	6+	A4:D4	96,195
D₄×A₄	Direct product of D₄ and A₄	12	6+	D4xA4	96,197
C₂²×S₄	Direct product of C₂² and S₄	12		C2^2xS4	96,226
C₂×C₂²⋊A₄	Direct product of C₂ and C₂²⋊A₄	12		C2xC2^2:A4	96,229

Groups of order 108

		d	ρ	Label	ID
C₃×C₃²⋊C₄	Direct product of C₃ and C₃²⋊C₄	12	4	C3xC3^2:C4	108,36
C₃³⋊C₄	2^nd semidirect product of C₃³ and C₄ acting faithfully	12	4	C3^3:C4	108,37
C₃×S₃²	Direct product of C₃, S₃ and S₃	12	4	C3xS3^2	108,38
C₃²⋊₄D₆	The semidirect product of C₃² and D₆ acting via D₆/C₃=C₂²	12	4	C3^2:4D6	108,40

Groups of order 144

		d	ρ	Label	ID
S₃²⋊C₄	The semidirect product of S₃² and C₄ acting via C₄/C₂=C₂	12	4+	S3^2:C4	144,115
C₆²⋊C₄	1^st semidirect product of C₆² and C₄ acting faithfully	12	4+	C6^2:C4	144,136
Dic₃⋊D₆	2^nd semidirect product of Dic₃ and D₆ acting via D₆/S₃=C₂; = Hol(Dic₃)	12	4+	Dic3:D6	144,154
S₃×S₄	Direct product of S₃ and S₄; = Hol(C₂×C₆)	12	6+	S3xS4	144,183
A₄²	Direct product of A₄ and A₄; = PΩ+₄(𝔽₃)	12	9+	A4^2	144,184
C₂×S₃≀C₂	Direct product of C₂ and S₃≀C₂	12	4+	C2xS3wrC2	144,186

Groups of order 192

		d	ρ	Label	ID
C₂³.₉S₄	3^rd non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	12	3	C2^3.9S4	192,182
C₄×C₄²⋊C₃	Direct product of C₄ and C₄²⋊C₃	12	3	C4xC4^2:C3	192,188
C₂⁴⋊C₁₂	1^st semidirect product of C₂⁴ and C₁₂ acting via C₁₂/C₂=C₆	12	6+	C2^4:C12	192,191
C₂³⋊₂D₄⋊C₃	The semidirect product of C₂³⋊₂D₄ and C₃ acting faithfully	12	6+	C2^3:2D4:C3	192,194
C₂⁴.₂A₄	2^nd non-split extension by C₂⁴ of A₄ acting faithfully	12	6+	C2^4.2A4	192,197
C₂×C₄²⋊S₃	Direct product of C₂ and C₄²⋊S₃	12	3	C2xC4^2:S3	192,944
C₄²⋊D₆	The semidirect product of C₄² and D₆ acting faithfully	12	6+	C4^2:D6	192,956
C₂×C₂⁴⋊C₆	Direct product of C₂ and C₂⁴⋊C₆	12	6+	C2xC2^4:C6	192,1000
C₂×C₂³.A₄	Direct product of C₂ and C₂³.A₄	12	6+	C2xC2^3.A4	192,1002
D₄×S₄	Direct product of D₄ and S₄	12	6+	D4xS4	192,1472
C₂⁴⋊₄Dic₃	3^rd semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₂=S₃	12	6+	C2^4:4Dic3	192,1495
C₂×C₂²⋊S₄	Direct product of C₂ and C₂²⋊S₄	12	6+	C2xC2^2:S4	192,1538
C₂²×C₂²⋊A₄	Direct product of C₂² and C₂²⋊A₄	12		C2^2xC2^2:A4	192,1540

Groups of order 216

		d	ρ	Label	ID
S₃×C₃²⋊C₄	Direct product of S₃ and C₃²⋊C₄	12	8+	S3xC3^2:C4	216,156
C₃×S₃≀C₂	Direct product of C₃ and S₃≀C₂	12	4	C3xS3wrC2	216,157
C₃³⋊D₄	2^nd semidirect product of C₃³ and D₄ acting faithfully	12	4	C3^3:D4	216,158
C₃²⋊₂D₁₂	The semidirect product of C₃² and D₁₂ acting via D₁₂/C₃=D₄	12	8+	C3^2:2D12	216,159
S₃³	Direct product of S₃, S₃ and S₃; = Hol(C₃×S₃)	12	8+	S3^3	216,162

Groups of order 240

		d	ρ	Label	ID
A₅⋊C₄	The semidirect product of A₅ and C₄ acting via C₄/C₂=C₂	12	4	A5:C4	240,91

Groups of order 288

		d	ρ	Label	ID
D₆≀C₂	Wreath product of D₆ by C₂	12	4+	D6wrC2	288,889
PSO₄⁺ (𝔽₃)	Projective special orthogonal group of + type on 𝔽₃⁴; = A₄ ⋊S₄ = Hol(A₄)	12	9+	PSO+(4,3)	288,1026

Groups of order 324

		d	ρ	Label	ID
C₃×C₃³⋊C₄	Direct product of C₃ and C₃³⋊C₄; = AΣL₁(𝔽₈₁)	12	4	C3xC3^3:C4	324,162
C₃×C₃²⋊₄D₆	Direct product of C₃ and C₃²⋊₄D₆	12	4	C3xC3^2:4D6	324,167

Groups of order 432

		d	ρ	Label	ID
S₃×S₃≀C₂	Direct product of S₃ and S₃≀C₂	12	8+	S3xS3wrC2	432,741

On 13 points

Groups of order 13

		d	ρ	Label	ID
C₁₃	Cyclic group	13	1	C13	13,1

Groups of order 26

		d	ρ	Label	ID
D₁₃	Dihedral group	13	2+	D13	26,1

Groups of order 39

		d	ρ	Label	ID
C₁₃⋊C₃	The semidirect product of C₁₃ and C₃ acting faithfully	13	3	C13:C3	39,1

Groups of order 52

		d	ρ	Label	ID
C₁₃⋊C₄	The semidirect product of C₁₃ and C₄ acting faithfully	13	4+	C13:C4	52,3

Groups of order 78

		d	ρ	Label	ID
C₁₃⋊C₆	The semidirect product of C₁₃ and C₆ acting faithfully	13	6+	C13:C6	78,1

Groups of order 156

		d	ρ	Label	ID
F₁₃	Frobenius group; = C₁₃ ⋊C₁₂ = AGL₁(𝔽₁₃) = Aut(D₁₃) = Hol(C₁₃)	13	12+	F13	156,7

On 14 points

Groups of order 14

		d	ρ	Label	ID
C₁₄	Cyclic group	14	1	C14	14,2

Groups of order 28

		d	ρ	Label	ID
D₁₄	Dihedral group; = C₂×D₇	14	2+	D14	28,3

Groups of order 42

		d	ρ	Label	ID
C₂×C₇⋊C₃	Direct product of C₂ and C₇⋊C₃	14	3	C2xC7:C3	42,2

Groups of order 84

		d	ρ	Label	ID
C₂×F₇	Direct product of C₂ and F₇; = Aut(D₁₄) = Hol(C₁₄)	14	6+	C2xF7	84,7

Groups of order 98

		d	ρ	Label	ID
C₇×D₇	Direct product of C₇ and D₇; = AΣL₁(𝔽₄₉)	14	2	C7xD7	98,3

Groups of order 112

		d	ρ	Label	ID
C₂×F₈	Direct product of C₂ and F₈	14	7+	C2xF8	112,41

Groups of order 196

		d	ρ	Label	ID
C₇²⋊C₄	The semidirect product of C₇² and C₄ acting faithfully	14	4+	C7^2:C4	196,8
D₇²	Direct product of D₇ and D₇	14	4+	D7^2	196,9

Groups of order 294

		d	ρ	Label	ID
C₇²⋊S₃	The semidirect product of C₇² and S₃ acting faithfully	14	3	C7^2:S3	294,7
C₇⋊₄F₇	2^nd semidirect product of C₇ and F₇ acting via F₇/D₇=C₃	14	6	C7:4F7	294,12

Groups of order 336

		d	ρ	Label	ID
C₂×GL₃(𝔽₂)	Direct product of C₂ and GL₃(𝔽₂)	14	3	C2xGL(3,2)	336,209
C₂×AΓL₁(𝔽₈)	Direct product of C₂ and AΓL₁(𝔽₈)	14	7+	C2xAGammaL(1,8)	336,210

Groups of order 392

		d	ρ	Label	ID
D₇≀C₂	Wreath product of D₇ by C₂	14	4+	D7wrC2	392,37

Groups of order 448

		d	ρ	Label	ID
C₂³⋊F₈	2^nd semidirect product of C₂³ and F₈ acting via F₈/C₂³=C₇	14	7+	C2^3:F8	448,1394

On 15 points

Groups of order 15

		d	ρ	Label	ID
C₁₅	Cyclic group	15	1	C15	15,1

Groups of order 30

		d	ρ	Label	ID
C₅×S₃	Direct product of C₅ and S₃	15	2	C5xS3	30,1
C₃×D₅	Direct product of C₃ and D₅	15	2	C3xD5	30,2
D₁₅	Dihedral group	15	2+	D15	30,3

Groups of order 60

		d	ρ	Label	ID
C₃×F₅	Direct product of C₃ and F₅	15	4	C3xF5	60,6
C₃⋊F₅	The semidirect product of C₃ and F₅ acting via F₅/D₅=C₂	15	4	C3:F5	60,7
S₃×D₅	Direct product of S₃ and D₅	15	4+	S3xD5	60,8

Groups of order 75

		d	ρ	Label	ID
C₅²⋊C₃	The semidirect product of C₅² and C₃ acting faithfully	15	3	C5^2:C3	75,2

Groups of order 120

		d	ρ	Label	ID
S₃×F₅	Direct product of S₃ and F₅; = Aut(D₁₅) = Hol(C₁₅)	15	8+	S3xF5	120,36

Groups of order 150

		d	ρ	Label	ID
C₅²⋊S₃	The semidirect product of C₅² and S₃ acting faithfully	15	3	C5^2:S3	150,5
C₅²⋊C₆	The semidirect product of C₅² and C₆ acting faithfully	15	6+	C5^2:C6	150,6

Groups of order 180

		d	ρ	Label	ID
C₃×A₅	Direct product of C₃ and A₅; = GL₂(𝔽₄)	15	3	C3xA5	180,19

Groups of order 300

		d	ρ	Label	ID
C₅²⋊Dic₃	The semidirect product of C₅² and Dic₃ acting faithfully	15	12+	C5^2:Dic3	300,23
C₅²⋊C₁₂	The semidirect product of C₅² and C₁₂ acting faithfully	15	12+	C5^2:C12	300,24
C₅²⋊D₆	The semidirect product of C₅² and D₆ acting faithfully	15	6+	C5^2:D6	300,25

Groups of order 360

		d	ρ	Label	ID
C₃×S₅	Direct product of C₃ and S₅	15	4	C3xS5	360,119
ΓL₂(𝔽₄)	Semilinear group on 𝔽₄²; = C₃ ⋊S₅	15	6	GammaL(2,4)	360,120
S₃×A₅	Direct product of S₃ and A₅	15	6+	S3xA5	360,121

Groups of order 375

		d	ρ	Label	ID
C₅×C₅²⋊C₃	Direct product of C₅ and C₅²⋊C₃; = AΣL₁(𝔽₁₂₅)	15	3	C5xC5^2:C3	375,6

Groups of order 405

		d	ρ	Label	ID
C₃⁴⋊C₅	The semidirect product of C₃⁴ and C₅ acting faithfully	15	5	C3^4:C5	405,15

On 16 points

Groups of order 16

		d	ρ	Label	ID
C₁₆	Cyclic group	16	1	C16	16,1
C₄²	Abelian group of type [4,4]	16		C4^2	16,2
C₄⋊C₄	The semidirect product of C₄ and C₄ acting via C₄/C₂=C₂	16		C4:C4	16,4
C₂×C₈	Abelian group of type [2,8]	16		C2xC8	16,5
Q₁₆	Generalised quaternion group; = C₈ .C₂ = Dic₄	16	2-	Q16	16,9
C₂²×C₄	Abelian group of type [2,2,4]	16		C2^2xC4	16,10
C₂×Q₈	Direct product of C₂ and Q₈	16		C2xQ8	16,12
C₂⁴	Elementary abelian group of type [2,2,2,2]	16		C2^4	16,14

Groups of order 32

		d	ρ	Label	ID
C₂²⋊C₈	The semidirect product of C₂² and C₈ acting via C₈/C₄=C₂	16		C2^2:C8	32,5
C₄.₁₀D₄	2^nd non-split extension by C₄ of D₄ acting via D₄/C₂²=C₂	16	4-	C4.10D4	32,8
D₄⋊C₄	1^st semidirect product of D₄ and C₄ acting via C₄/C₂=C₂	16		D4:C4	32,9
C₈.C₄	1^st non-split extension by C₈ of C₄ acting via C₄/C₂=C₂	16	2	C8.C4	32,15
M₅(2)	Modular maximal-cyclic group; = C₁₆ ⋊₃ C₂	16	2	M5(2)	32,17
D₁₆	Dihedral group	16	2+	D16	32,18
SD₃₂	Semidihedral group; = C₁₆ ⋊₂ C₂ = QD₃₂	16	2	SD32	32,19
C₂×C₂²⋊C₄	Direct product of C₂ and C₂²⋊C₄	16		C2xC2^2:C4	32,22
C₄²⋊C₂	1^st semidirect product of C₄² and C₂ acting faithfully	16		C4^2:C2	32,24
C₄×D₄	Direct product of C₄ and D₄	16		C4xD4	32,25
C₄⋊D₄	The semidirect product of C₄ and D₄ acting via D₄/C₂²=C₂	16		C4:D4	32,28
C₂²⋊Q₈	The semidirect product of C₂² and Q₈ acting via Q₈/C₄=C₂	16		C2^2:Q8	32,29
C₂².D₄	3^rd non-split extension by C₂² of D₄ acting via D₄/C₂²=C₂	16		C2^2.D4	32,30
C₄.₄D₄	4^th non-split extension by C₄ of D₄ acting via D₄/C₄=C₂	16		C4.4D4	32,31
C₄²⋊₂C₂	2^nd semidirect product of C₄² and C₂ acting faithfully	16		C4^2:2C2	32,33
C₄⋊₁D₄	The semidirect product of C₄ and D₄ acting via D₄/C₄=C₂	16		C4:1D4	32,34
C₂×M₄(2)	Direct product of C₂ and M₄(2)	16		C2xM4(2)	32,37
C₈○D₄	Central product of C₈ and D₄	16	2	C8oD4	32,38
C₂×D₈	Direct product of C₂ and D₈	16		C2xD8	32,39
C₂×SD₁₆	Direct product of C₂ and SD₁₆	16		C2xSD16	32,40
C₄○D₈	Central product of C₄ and D₈	16	2	C4oD8	32,42
C₈.C₂²	The non-split extension by C₈ of C₂² acting faithfully	16	4-	C8.C2^2	32,44
C₂²×D₄	Direct product of C₂² and D₄	16		C2^2xD4	32,46
C₂×C₄○D₄	Direct product of C₂ and C₄○D₄	16		C2xC4oD4	32,48
2_-¹⁺⁴	Gamma matrices = Extraspecial group; = D₄ ○Q₈	16	4-	ES-(2,2)	32,50

Groups of order 48

		d	ρ	Label	ID
CSU₂(𝔽₃)	Conformal special unitary group on 𝔽₃²; = Q₈ .S₃ = 2O = <2,3,4>	16	2-	CSU(2,3)	48,28
C₂×SL₂(𝔽₃)	Direct product of C₂ and SL₂(𝔽₃)	16		C2xSL(2,3)	48,32
C₄.A₄	The central extension by C₄ of A₄	16	2	C4.A4	48,33

Groups of order 64

		d	ρ	Label	ID
C₂³⋊C₈	The semidirect product of C₂³ and C₈ acting via C₈/C₂=C₄	16		C2^3:C8	64,4
C₂².SD₁₆	1^st non-split extension by C₂² of SD₁₆ acting via SD₁₆/Q₈=C₂	16		C2^2.SD16	64,8
C₂³.₃₁D₄	2^nd non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	16		C2^3.31D4	64,9
C₄.₉C₄²	1^st central stem extension by C₄ of C₄²	16	4	C4.9C4^2	64,18
C₄.₁₀C₄²	2^nd central stem extension by C₄ of C₄²	16	4	C4.10C4^2	64,19
C₄²⋊₆C₄	3^rd semidirect product of C₄² and C₄ acting via C₄/C₂=C₂	16		C4^2:6C4	64,20
C₂³.₉D₄	2^nd non-split extension by C₂³ of D₄ acting via D₄/C₂=C₂²	16		C2^3.9D4	64,23
M₄(2)⋊₄C₄	4^th semidirect product of M₄(2) and C₄ acting via C₄/C₂=C₂	16	4	M4(2):4C4	64,25
C₁₆⋊C₄	2^nd semidirect product of C₁₆ and C₄ acting faithfully	16	4	C16:C4	64,28
C₂³.C₈	The non-split extension by C₂³ of C₈ acting via C₈/C₂=C₄	16	4	C2^3.C8	64,30
C₂³.D₄	2^nd non-split extension by C₂³ of D₄ acting faithfully	16	4	C2^3.D4	64,33
C₄²⋊₃C₄	3^rd semidirect product of C₄² and C₄ acting faithfully	16	4	C4^2:3C4	64,35
C₄².C₄	2^nd non-split extension by C₄² of C₄ acting faithfully	16	4	C4^2.C4	64,36
C₄².₃C₄	3^rd non-split extension by C₄² of C₄ acting faithfully	16	4-	C4^2.3C4	64,37
D₈⋊₂C₄	2^nd semidirect product of D₈ and C₄ acting via C₄/C₂=C₂	16	4	D8:2C4	64,41
M₅(2)⋊C₂	6^th semidirect product of M₅(2) and C₂ acting faithfully	16	4+	M5(2):C2	64,42
C₈.C₈	1^st non-split extension by C₈ of C₈ acting via C₈/C₄=C₂	16	2	C8.C8	64,45
C₈.Q₈	The non-split extension by C₈ of Q₈ acting via Q₈/C₂=C₂²	16	4	C8.Q8	64,46
C₂⁴⋊₃C₄	1^st semidirect product of C₂⁴ and C₄ acting via C₄/C₂=C₂	16		C2^4:3C4	64,60
C₂⁴.₄C₄	2^nd non-split extension by C₂⁴ of C₄ acting via C₄/C₂=C₂	16		C2^4.4C4	64,88
C₂×C₂³⋊C₄	Direct product of C₂ and C₂³⋊C₄	16		C2xC2^3:C4	64,90
C₂³.C₂³	2^nd non-split extension by C₂³ of C₂³ acting via C₂³/C₂=C₂²	16	4	C2^3.C2^3	64,91
C₂×C₄.D₄	Direct product of C₂ and C₄.D₄	16		C2xC4.D4	64,92
M₄(2).₈C₂²	3^rd non-split extension by M₄(2) of C₂² acting via C₂²/C₂=C₂	16	4	M4(2).8C2^2	64,94
C₂³.₃₇D₄	8^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	16		C2^3.37D4	64,99
C₂×C₄≀C₂	Direct product of C₂ and C₄≀C₂	16		C2xC4wrC2	64,101
C₄²⋊C₂²	1^st semidirect product of C₄² and C₂² acting faithfully	16	4	C4^2:C2^2	64,102
M₄(2).C₄	1^st non-split extension by M₄(2) of C₄ acting via C₄/C₂=C₂	16	4	M4(2).C4	64,111
C₈○D₈	Central product of C₈ and D₈	16	2	C8oD8	64,124
C₈.₂₆D₄	13^rd non-split extension by C₈ of D₄ acting via D₄/C₂²=C₂	16	4	C8.26D4	64,125
C₂²⋊D₈	The semidirect product of C₂² and D₈ acting via D₈/D₄=C₂	16		C2^2:D8	64,128
C₂²⋊SD₁₆	The semidirect product of C₂² and SD₁₆ acting via SD₁₆/D₄=C₂	16		C2^2:SD16	64,131
D₄.₈D₄	3^rd non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	16	4	D4.8D4	64,135
D₄.₉D₄	4^th non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	16	4	D4.9D4	64,136
D₄.₁₀D₄	5^th non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	16	4-	D4.10D4	64,137
C₂³.₇D₄	7^th non-split extension by C₂³ of D₄ acting faithfully	16	4	C2^3.7D4	64,139
D₄.₃D₄	3^rd non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	16	4	D4.3D4	64,152
D₄.₄D₄	4^th non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	16	4+	D4.4D4	64,153
C₁₆⋊C₂²	The semidirect product of C₁₆ and C₂² acting faithfully	16	4+	C16:C2^2	64,190
C₂².₁₁C₂⁴	7^th central extension by C₂² of C₂⁴	16		C2^2.11C2^4	64,199
C₂×C₂²≀C₂	Direct product of C₂ and C₂²≀C₂	16		C2xC2^2wrC2	64,202
C₂².₁₉C₂⁴	5^th central stem extension by C₂² of C₂⁴	16		C2^2.19C2^4	64,206
C₂³⋊₃D₄	2^nd semidirect product of C₂³ and D₄ acting via D₄/C₂=C₂²	16		C2^3:3D4	64,215
C₂².₂₉C₂⁴	15^th central stem extension by C₂² of C₂⁴	16		C2^2.29C2^4	64,216
C₂².₃₂C₂⁴	18^th central stem extension by C₂² of C₂⁴	16		C2^2.32C2^4	64,219
C₂³⋊₂Q₈	2^nd semidirect product of C₂³ and Q₈ acting via Q₈/C₂=C₂²	16		C2^3:2Q8	64,224
D₄²	Direct product of D₄ and D₄	16		D4^2	64,226
D₄⋊₅D₄	1^st semidirect product of D₄ and D₄ acting through Inn(D₄)	16		D4:5D4	64,227
C₂².₄₅C₂⁴	31^st central stem extension by C₂² of C₂⁴	16		C2^2.45C2^4	64,232
C₂².₅₄C₂⁴	40^th central stem extension by C₂² of C₂⁴	16		C2^2.54C2^4	64,241
C₂⁴⋊C₂²	4^th semidirect product of C₂⁴ and C₂² acting faithfully	16		C2^4:C2^2	64,242
Q₈○M₄(2)	Central product of Q₈ and M₄(2)	16	4	Q8oM4(2)	64,249
C₂×C₈⋊C₂²	Direct product of C₂ and C₈⋊C₂²	16		C2xC8:C2^2	64,254
D₈⋊C₂²	4^th semidirect product of D₈ and C₂² acting via C₂²/C₂=C₂	16	4	D8:C2^2	64,256
D₄○D₈	Central product of D₄ and D₈	16	4+	D4oD8	64,257
D₄○SD₁₆	Central product of D₄ and SD₁₆	16	4	D4oSD16	64,258
C₂×2₊¹⁺⁴	Direct product of C₂ and 2₊¹⁺⁴	16		C2xES+(2,2)	64,264
C₂.C₂⁵	6^th central stem extension by C₂ of C₂⁵	16	4	C2.C2^5	64,266

Groups of order 96

		d	ρ	Label	ID
C₄²⋊C₆	1^st semidirect product of C₄² and C₆ acting faithfully	16	6	C4^2:C6	96,71
C₂×GL₂(𝔽₃)	Direct product of C₂ and GL₂(𝔽₃)	16		C2xGL(2,3)	96,189
Q₈.D₆	2^nd non-split extension by Q₈ of D₆ acting via D₆/C₂=S₃	16	4-	Q8.D6	96,190
C₄.₆S₄	3^rd central extension by C₄ of S₄	16	2	C4.6S4	96,192
C₄.₃S₄	3^rd non-split extension by C₄ of S₄ acting via S₄/A₄=C₂	16	4+	C4.3S4	96,193
D₄.A₄	The non-split extension by D₄ of A₄ acting through Inn(D₄)	16	4-	D4.A4	96,202

Groups of order 128

		d	ρ	Label	ID
C₂⁴.₄Q₈	3^rd non-split extension by C₂⁴ of Q₈ acting via Q₈/C₂=C₂²	16		C2^4.4Q8	128,36
C₂⁴⋊C₈	1^st semidirect product of C₂⁴ and C₈ acting via C₈/C₂=C₄	16		C2^4:C8	128,48
C₂⁴.C₈	2^nd non-split extension by C₂⁴ of C₈ acting via C₈/C₂=C₄	16	4	C2^4.C8	128,52
C₄².C₈	1^st non-split extension by C₄² of C₈ acting via C₈/C₂=C₄	16	4	C4^2.C8	128,59
C₈≀C₂	Wreath product of C₈ by C₂	16	2	C8wrC2	128,67
C₈.₃₂D₈	9^th non-split extension by C₈ of D₈ acting via D₈/D₄=C₂	16	4	C8.32D8	128,68
C₂³.D₈	1^st non-split extension by C₂³ of D₈ acting via D₈/C₂=D₄	16	8+	C2^3.D8	128,71
C₂³.SD₁₆	1^st non-split extension by C₂³ of SD₁₆ acting via SD₁₆/C₂=D₄	16	8+	C2^3.SD16	128,73
C₂⁴.D₄	1^st non-split extension by C₂⁴ of D₄ acting faithfully	16		C2^4.D4	128,75
C₄.C₄≀C₂	9^th non-split extension by C₄ of C₄≀C₂ acting via C₄≀C₂/C₄²=C₂	16	8+	C4.C4wrC2	128,87
C₈.₂₄D₈	1^st non-split extension by C₈ of D₈ acting via D₈/D₄=C₂	16	4+	C8.24D8	128,89
C₈.₂₉D₈	6^th non-split extension by C₈ of D₈ acting via D₈/D₄=C₂	16	4	C8.29D8	128,91
C₄².D₄	1^st non-split extension by C₄² of D₄ acting faithfully	16	4+	C4^2.D4	128,134
C₄².₂D₄	2^nd non-split extension by C₄² of D₄ acting faithfully	16	4	C4^2.2D4	128,135
C₄².₃D₄	3^rd non-split extension by C₄² of D₄ acting faithfully	16	4	C4^2.3D4	128,136
C₄².₄D₄	4^th non-split extension by C₄² of D₄ acting faithfully	16	4-	C4^2.4D4	128,137
C₈⋊C₄⋊C₄	1^st semidirect product of C₈⋊C₄ and C₄ acting faithfully	16	8+	C8:C4:C4	128,138
C₄⋊₁D₄⋊C₄	2^nd semidirect product of C₄⋊₁D₄ and C₄ acting faithfully	16	4+	C4:1D4:C4	128,140
(C₄×C₈)⋊₆C₄	6^th semidirect product of C₄×C₈ and C₄ acting faithfully	16	4	(C4xC8):6C4	128,141
(C₄×C₈).C₄	6^th non-split extension by C₄×C₈ of C₄ acting faithfully	16	4	(C4xC8).C4	128,142
C₈⋊C₄⋊₅C₄	5^th semidirect product of C₈⋊C₄ and C₄ acting faithfully	16	8+	C8:C4:5C4	128,144
C₂⁵.₃C₄	3^rd non-split extension by C₂⁵ of C₄ acting faithfully	16		C2^5.3C4	128,194
C₂⁴.₁₅₀D₄	5^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂²=C₂	16		C2^4.150D4	128,236
C₂³⋊D₈	The semidirect product of C₂³ and D₈ acting via D₈/C₂=D₄	16		C2^3:D8	128,327
C₂³⋊SD₁₆	1^st semidirect product of C₂³ and SD₁₆ acting via SD₁₆/C₂=D₄	16		C2^3:SD16	128,328
C₂⁴.₉D₄	9^th non-split extension by C₂⁴ of D₄ acting faithfully	16		C2^4.9D4	128,332
C₂⁵⋊C₄	1^st semidirect product of C₂⁵ and C₄ acting faithfully	16		C2^5:C4	128,513
C₂⁵.C₄	4^th non-split extension by C₂⁵ of C₄ acting faithfully	16		C2^5.C4	128,515
C₄○D₄.D₄	3^rd non-split extension by C₄○D₄ of D₄ acting via D₄/C₂=C₂²	16	8+	C4oD4.D4	128,527
C₂⁴.₆₈D₄	23^rd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	16		C2^4.68D4	128,551
(C₂×C₄²)⋊C₄	8^th semidirect product of C₂×C₄² and C₄ acting faithfully	16	4	(C2xC4^2):C4	128,559
C₂⁴.C₂³	1^st non-split extension by C₂⁴ of C₂³ acting faithfully	16	8+	C2^4.C2^3	128,560
C₂⁴.₆(C₂×C₄)	6^th non-split extension by C₂⁴ of C₂×C₄ acting faithfully	16	8+	C2^4.6(C2xC4)	128,561
C₈⋊C₄⋊₁₇C₄	12^nd semidirect product of C₈⋊C₄ and C₄ acting via C₄/C₂=C₂	16	4	C8:C4:17C4	128,573
M₄(2).₄₁D₄	5^th non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	16	4	M4(2).41D4	128,593
M₄(2)⋊₁₉D₄	6^th semidirect product of M₄(2) and D₄ acting via D₄/C₂²=C₂	16	4	M4(2):19D4	128,616
C₂⁴.₂₄D₄	24^th non-split extension by C₂⁴ of D₄ acting faithfully	16		C2^4.24D4	128,619
C₂⁵.C₂²	9^th non-split extension by C₂⁵ of C₂² acting faithfully	16		C2^5.C2^2	128,621
(C₂×C₈)⋊D₄	3^rd semidirect product of C₂×C₈ and D₄ acting faithfully	16	4	(C2xC8):D4	128,623
(C₂×C₄)≀C₂	Wreath product of C₂×C₄ by C₂	16		(C2xC4)wrC2	128,628
C₂⁴.₇₈D₄	33^rd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	16		C2^4.78D4	128,630
M₄(2).₄₇D₄	11^st non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	16	8+	M4(2).47D4	128,635
C₄².₅D₄	5^th non-split extension by C₄² of D₄ acting faithfully	16	8+	C4^2.5D4	128,636
C₄².₄₂₆D₄	59^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	16	4	C4^2.426D4	128,638
(C₂×C₈)⋊₄D₄	4^th semidirect product of C₂×C₈ and D₄ acting faithfully	16	8+	(C2xC8):4D4	128,642
C₄²⋊D₄	1^st semidirect product of C₄² and D₄ acting faithfully	16	8+	C4^2:D4	128,643
C₂⁴.₂₈D₄	28^th non-split extension by C₂⁴ of D₄ acting faithfully	16	8+	C2^4.28D4	128,645
M₄(2)⋊₂₁D₄	8^th semidirect product of M₄(2) and D₄ acting via D₄/C₂²=C₂	16	8+	M4(2):21D4	128,646
C₄².₄₂₇D₄	60^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	16	4	C4^2.427D4	128,664
C₄²⋊₉D₄	3^rd semidirect product of C₄² and D₄ acting via D₄/C₂=C₂²	16		C4^2:9D4	128,734
M₄(2)⋊₅D₄	5^th semidirect product of M₄(2) and D₄ acting via D₄/C₂=C₂²	16	8+	M4(2):5D4	128,740
C₄²⋊₂D₄	2^nd semidirect product of C₄² and D₄ acting faithfully	16	4	C4^2:2D4	128,742
C₂⁴⋊D₄	1^st semidirect product of C₂⁴ and D₄ acting faithfully	16		C2^4:D4	128,753
C₂⁴⋊₂Q₈	1^st semidirect product of C₂⁴ and Q₈ acting via Q₈/C₂=C₂²	16		C2^4:2Q8	128,761
C₄².₈D₄	8^th non-split extension by C₄² of D₄ acting faithfully	16	4	C4^2.8D4	128,763
C₂⁴⋊Q₈	The semidirect product of C₂⁴ and Q₈ acting faithfully	16	8+	C2^4:Q8	128,764
M₄(2).₈D₄	8^th non-split extension by M₄(2) of D₄ acting via D₄/C₂=C₂²	16	8+	M4(2).8D4	128,780
C₄².₁₃₁D₄	113^rd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	16	4	C4^2.131D4	128,782
C₂⁴.Q₈	The non-split extension by C₂⁴ of Q₈ acting faithfully	16	8+	C2^4.Q8	128,801
(C₂×C₈).D₄	5^th non-split extension by C₂×C₈ of D₄ acting faithfully	16	8+	(C2xC8).D4	128,813
C₂⁴.₁₁Q₈	10^th non-split extension by C₂⁴ of Q₈ acting via Q₈/C₂=C₂²	16	4	C2^4.11Q8	128,823
C₄².₃₂Q₈	32^nd non-split extension by C₄² of Q₈ acting via Q₈/C₂=C₂²	16	4	C4^2.32Q8	128,834
C₂⁴.₄C₂³	4^th non-split extension by C₂⁴ of C₂³ acting faithfully	16	8+	C2^4.4C2^3	128,836
C₂×C₂≀C₄	Direct product of C₂ and C₂≀C₄	16		C2xC2wrC4	128,850
C₄○C₂≀C₄	Central product of C₄ and C₂≀C₄	16	4	C4oC2wrC4	128,852
C₂⁴.₃₆D₄	36^th non-split extension by C₂⁴ of D₄ acting faithfully	16	8+	C2^4.36D4	128,853
C₂≀C₄⋊C₂	6^th semidirect product of C₂≀C₄ and C₂ acting faithfully	16	8+	C2wrC4:C2	128,854
C₂×C₄²⋊C₄	Direct product of C₂ and C₄²⋊C₄	16		C2xC4^2:C4	128,856
C₄⋊Q₈⋊₂₉C₄	24^th semidirect product of C₄⋊Q₈ and C₄ acting via C₄/C₂=C₂	16	4	C4:Q8:29C4	128,858
C₂⁴.₃₉D₄	39^th non-split extension by C₂⁴ of D₄ acting faithfully	16	8+	C2^4.39D4	128,859
C₄.₄D₄⋊C₄	6^th semidirect product of C₄.₄D₄ and C₄ acting faithfully	16	8+	C4.4D4:C4	128,860
(C₂×D₄).₁₃₅D₄	97^th non-split extension by C₂×D₄ of D₄ acting via D₄/C₂=C₂²	16	4	(C2xD4).135D4	128,864
C₄⋊₁D₄.C₄	5^th non-split extension by C₄⋊₁D₄ of C₄ acting faithfully	16	8+	C4:1D4.C4	128,866
C₈.₅M₄(2)	5^th non-split extension by C₈ of M₄(2) acting via M₄(2)/C₄=C₂²	16	4	C8.5M4(2)	128,897
D₁₆⋊C₄	The semidirect product of D₁₆ and C₄ acting faithfully; = Aut(D₁₆) = Hol(C₁₆)	16	8+	D16:C4	128,913
D₈⋊D₄	The semidirect product of D₈ and D₄ acting via D₄/C₂=C₂²	16	8+	D8:D4	128,922
C₄²⋊₄D₄	4^th semidirect product of C₄² and D₄ acting faithfully	16	4	C4^2:4D4	128,929
C₄².₁₃D₄	13^rd non-split extension by C₄² of D₄ acting faithfully	16	4	C4^2.13D4	128,930
C₄²⋊₅D₄	5^th semidirect product of C₄² and D₄ acting faithfully	16	8+	C4^2:5D4	128,931
C₄²⋊₆D₄	6^th semidirect product of C₄² and D₄ acting faithfully	16	8+	C4^2:6D4	128,932
C₄².₁₅D₄	15^th non-split extension by C₄² of D₄ acting faithfully	16	8+	C4^2.15D4	128,934
C₄².₁₇D₄	17^th non-split extension by C₄² of D₄ acting faithfully	16	4	C4^2.17D4	128,936
Q₈≀C₂	Wreath product of Q₈ by C₂	16	4-	Q8wrC2	128,937
D₈⋊₃D₄	2^nd semidirect product of D₈ and D₄ acting via D₄/C₄=C₂	16	4+	D8:3D4	128,945
D₈⋊₃Q₈	3^rd semidirect product of D₈ and Q₈ acting via Q₈/C₄=C₂	16	4	D8:3Q8	128,962
M₅(2).C₂²	8^th non-split extension by M₅(2) of C₂² acting faithfully	16	8+	M5(2).C2^2	128,970
C₂³≀C₂	Wreath product of C₂³ by C₂	16		C2^3wrC2	128,1578
C₂³.C₂⁴	3^rd non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	16	8+	C2^3.C2^4	128,1615
M₄(2).₂₄C₂³	6^th non-split extension by M₄(2) of C₂³ acting via C₂³/C₂²=C₂	16	8+	M4(2).24C2^3	128,1620
2_-¹⁺⁴⋊₅C₄	4^th semidirect product of 2_-¹⁺⁴ and C₄ acting via C₄/C₂=C₂	16	4	ES-(2,2):5C4	128,1633
M₄(2).₅₁D₄	1^st non-split extension by M₄(2) of D₄ acting through Inn(M₄(2))	16	4	M4(2).51D4	128,1688
C₂⁴.₁₇₇D₄	32^nd non-split extension by C₂⁴ of D₄ acting via D₄/C₂²=C₂	16		C2^4.177D4	128,1735
C₂×D₄⋊₄D₄	Direct product of C₂ and D₄⋊₄D₄	16		C2xD4:4D4	128,1746
C₄².₃₁₃C₂³	174^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	16	4	C4^2.313C2^3	128,1750
M₄(2)⋊C₂³	3^rd semidirect product of M₄(2) and C₂³ acting via C₂³/C₂=C₂²	16	8+	M4(2):C2^3	128,1751
C₄².₁₂C₂³	12^nd non-split extension by C₄² of C₂³ acting faithfully	16	8+	C4^2.12C2^3	128,1753
C₂×C₂≀C₂²	Direct product of C₂ and C₂≀C₂²	16		C2xC2wrC2^2	128,1755
C₂³.₇C₂⁴	7^th non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	16	4	C2^3.7C2^4	128,1757
C₂⁴⋊C₂³	2^nd semidirect product of C₂⁴ and C₂³ acting faithfully	16	8+	C2^4:C2^3	128,1758
C₂³.₉C₂⁴	9^th non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	16	8+	C2^3.9C2^4	128,1759
M₄(2).₃₇D₄	1^st non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	16	8+	M4(2).37D4	128,1800
D₈⋊₁₁D₄	5^th semidirect product of D₈ and D₄ acting via D₄/C₂²=C₂	16	8+	D8:11D4	128,2020
D₈⋊₆D₄	5^th semidirect product of D₈ and D₄ acting via D₄/C₄=C₂	16	4	D8:6D4	128,2023
D₈○D₈	Central product of D₈ and D₈	16	4+	D8oD8	128,2024
C₂².₇₃C₂⁵	54^th central stem extension by C₂² of C₂⁵	16		C2^2.73C2^5	128,2216
C₂².₇₉C₂⁵	60^th central stem extension by C₂² of C₂⁵	16		C2^2.79C2^5	128,2222
C₄²⋊C₂³	4^th semidirect product of C₄² and C₂³ acting faithfully	16		C4^2:C2^3	128,2264
D₈⋊C₂³	6^th semidirect product of D₈ and C₂³ acting via C₂³/C₂²=C₂	16	8+	D8:C2^3	128,2317
2₊¹⁺⁶	Extraspecial group; = D₄ ○2₊¹⁺⁴	16	8+	ES+(2,3)	128,2326

Groups of order 192

		d	ρ	Label	ID
C₂³.SL₂(𝔽₃)	1^st non-split extension by C₂³ of SL₂(𝔽₃) acting via SL₂(𝔽₃)/C₂=A₄	16	4	C2^3.SL(2,3)	192,4
C₂⁴⋊Dic₃	The semidirect product of C₂⁴ and Dic₃ acting faithfully	16	12+	C2^4:Dic3	192,184
C₄²⋊Dic₃	The semidirect product of C₄² and Dic₃ acting faithfully	16	12+	C4^2:Dic3	192,185
2₊¹⁺⁴.C₆	1^st non-split extension by 2₊¹⁺⁴ of C₆ acting faithfully	16	4	ES+(2,2).C6	192,202
C₂⁴.₆A₄	6^th non-split extension by C₂⁴ of A₄ acting faithfully	16	12+	C2^4.6A4	192,1008
C₂⁴⋊A₄	3^rd semidirect product of C₂⁴ and A₄ acting faithfully	16	12+	C2^4:A4	192,1009
C₂⁴.₇A₄	7^th non-split extension by C₂⁴ of A₄ acting faithfully	16		C2^4.7A4	192,1021
C₄²⋊A₄	The semidirect product of C₄² and A₄ acting faithfully	16	12+	C4^2:A4	192,1023
C₂⁴⋊₅A₄	5^th semidirect product of C₂⁴ and A₄ acting faithfully	16		C2^4:5A4	192,1024
D₄.₄S₄	1^st non-split extension by D₄ of S₄ acting through Inn(D₄)	16	4	D4.4S4	192,1485
C₂³.S₄	4^th non-split extension by C₂³ of S₄ acting faithfully	16	4	C2^3.S4	192,1491
Q₈.S₄	2^nd non-split extension by Q₈ of S₄ acting via S₄/C₂²=S₃	16	4	Q8.S4	192,1492
C₂×C₂³⋊A₄	Direct product of C₂ and C₂³⋊A₄	16		C2xC2^3:A4	192,1508
2₊¹⁺⁴.₃C₆	The non-split extension by 2₊¹⁺⁴ of C₆ acting via C₆/C₂=C₃	16	4	ES+(2,2).3C6	192,1509

Groups of order 240

		d	ρ	Label	ID
F₁₆	Frobenius group; = C₂⁴ ⋊C₁₅ = AGL₁(𝔽₁₆)	16	15+	F16	240,191

Groups of order 288

		d	ρ	Label	ID
A₄×S₄	Direct product of A₄ and S₄	16	9+	A4xS4	288,1024

Groups of order 336

		d	ρ	Label	ID
SL₂(𝔽₇)	Special linear group on 𝔽₇²; = C₂ .GL₃(𝔽₂)	16	4	SL(2,7)	336,114

Groups of order 480

		d	ρ	Label	ID
F₁₆⋊C₂	The semidirect product of F₁₆ and C₂ acting faithfully	16	15+	F16:C2	480,1188

On 17 points

Groups of order 17

		d	ρ	Label	ID
C₁₇	Cyclic group	17	1	C17	17,1

Groups of order 34

		d	ρ	Label	ID
D₁₇	Dihedral group	17	2+	D17	34,1

Groups of order 68

		d	ρ	Label	ID
C₁₇⋊C₄	The semidirect product of C₁₇ and C₄ acting faithfully	17	4+	C17:C4	68,3

Groups of order 136

		d	ρ	Label	ID
C₁₇⋊C₈	The semidirect product of C₁₇ and C₈ acting faithfully	17	8+	C17:C8	136,12

Groups of order 272

		d	ρ	Label	ID
F₁₇	Frobenius group; = C₁₇ ⋊C₁₆ = AGL₁(𝔽₁₇) = Aut(D₁₇) = Hol(C₁₇)	17	16+	F17	272,50

On 18 points

Groups of order 18

		d	ρ	Label	ID
C₁₈	Cyclic group	18	1	C18	18,2
C₃×C₆	Abelian group of type [3,6]	18		C3xC6	18,5

Groups of order 36

		d	ρ	Label	ID
C₃.A₄	The central extension by C₃ of A₄	18	3	C3.A4	36,3
D₁₈	Dihedral group; = C₂×D₉	18	2+	D18	36,4
C₂×C₃⋊S₃	Direct product of C₂ and C₃⋊S₃	18		C2xC3:S3	36,13

Groups of order 54

		d	ρ	Label	ID
C₃×D₉	Direct product of C₃ and D₉	18	2	C3xD9	54,3
S₃×C₉	Direct product of C₉ and S₃	18	2	S3xC9	54,4
C₂×He₃	Direct product of C₂ and He₃	18	3	C2xHe3	54,10
C₂×3_-¹⁺²	Direct product of C₂ and 3_-¹⁺²	18	3	C2xES-(3,1)	54,11
S₃×C₃²	Direct product of C₃² and S₃	18		S3xC3^2	54,12
C₃×C₃⋊S₃	Direct product of C₃ and C₃⋊S₃	18		C3xC3:S3	54,13

Groups of order 72

		d	ρ	Label	ID
C₃.S₄	The non-split extension by C₃ of S₄ acting via S₄/A₄=C₂	18	6+	C3.S4	72,15
C₂×C₃.A₄	Direct product of C₂ and C₃.A₄	18	3	C2xC3.A4	72,16
C₆×A₄	Direct product of C₆ and A₄	18	3	C6xA4	72,47

Groups of order 108

		d	ρ	Label	ID
He₃⋊C₄	The semidirect product of He₃ and C₄ acting faithfully	18	3	He3:C4	108,15
S₃×D₉	Direct product of S₃ and D₉	18	4+	S3xD9	108,16
C₃².A₄	The non-split extension by C₃² of A₄ acting via A₄/C₂²=C₃	18	3	C3^2.A4	108,21
C₃²⋊A₄	The semidirect product of C₃² and A₄ acting via A₄/C₂²=C₃	18	3	C3^2:A4	108,22
C₂×C₃²⋊C₆	Direct product of C₂ and C₃²⋊C₆	18	6+	C2xC3^2:C6	108,25
C₂×C₉⋊C₆	Direct product of C₂ and C₉⋊C₆; = Aut(D₁₈) = Hol(C₁₈)	18	6+	C2xC9:C6	108,26
C₂×He₃⋊C₂	Direct product of C₂ and He₃⋊C₂	18	3	C2xHe3:C2	108,28
S₃×C₃⋊S₃	Direct product of S₃ and C₃⋊S₃	18		S3xC3:S3	108,39

Groups of order 144

		d	ρ	Label	ID
C₂×C₃.S₄	Direct product of C₂ and C₃.S₄	18	6+	C2xC3.S4	144,109
C₂×F₉	Direct product of C₂ and F₉	18	8+	C2xF9	144,185
C₂×PSU₃(𝔽₂)	Direct product of C₂ and PSU₃(𝔽₂)	18	8+	C2xPSU(3,2)	144,187
C₆×S₄	Direct product of C₆ and S₄	18	3	C6xS4	144,188
C₂×C₃⋊S₄	Direct product of C₂ and C₃⋊S₄	18	6+	C2xC3:S4	144,189
C₂×S₃×A₄	Direct product of C₂, S₃ and A₄	18	6+	C2xS3xA4	144,190

Groups of order 162

		d	ρ	Label	ID
C₉×D₉	Direct product of C₉ and D₉	18	2	C9xD9	162,3
C₃²⋊C₁₈	The semidirect product of C₃² and C₁₈ acting via C₁₈/C₃=C₆	18	6	C3^2:C18	162,4
C₉⋊C₁₈	The semidirect product of C₉ and C₁₈ acting via C₁₈/C₃=C₆	18	6	C9:C18	162,6
C₃²⋊₂D₉	2^nd semidirect product of C₃² and D₉ acting via D₉/C₃=S₃	18	6	C3^2:2D9	162,17
C₂×C₃≀C₃	Direct product of C₂ and C₃≀C₃	18	3	C2xC3wrC3	162,28
C₃×C₃²⋊C₆	Direct product of C₃ and C₃²⋊C₆	18	6	C3xC3^2:C6	162,34
S₃×He₃	Direct product of S₃ and He₃	18	6	S3xHe3	162,35
C₃×C₉⋊C₆	Direct product of C₃ and C₉⋊C₆	18	6	C3xC9:C6	162,36
S₃×3_-¹⁺²	Direct product of S₃ and 3_-¹⁺²	18	6	S3xES-(3,1)	162,37
He₃⋊₅S₃	2^nd semidirect product of He₃ and S₃ acting via S₃/C₃=C₂	18	6	He3:5S3	162,46
C₃²×C₃⋊S₃	Direct product of C₃² and C₃⋊S₃	18		C3^2xC3:S3	162,52

Groups of order 216

		d	ρ	Label	ID
He₃⋊D₄	The semidirect product of He₃ and D₄ acting faithfully	18	6+	He3:D4	216,87
C₃².S₄	The non-split extension by C₃² of S₄ acting via S₄/C₂²=S₃	18	6+	C3^2.S4	216,90
C₆²⋊S₃	4^th semidirect product of C₆² and S₃ acting faithfully	18	6+	C6^2:S3	216,92
C₃²⋊S₄	2^nd semidirect product of C₃² and S₄ acting via S₄/C₂²=S₃	18	3	C3^2:S4	216,95
C₆²⋊C₆	3^rd semidirect product of C₆² and C₆ acting faithfully	18	6+	C6^2:C6	216,99
C₂×C₃²⋊D₆	Direct product of C₂ and C₃²⋊D₆	18	6+	C2xC3^2:D6	216,102
C₂×C₃².A₄	Direct product of C₂ and C₃².A₄	18	3	C2xC3^2.A4	216,106
C₂×C₃²⋊A₄	Direct product of C₂ and C₃²⋊A₄	18	3	C2xC3^2:A4	216,107

Groups of order 288

		d	ρ	Label	ID
C₂×AΓL₁(𝔽₉)	Direct product of C₂ and AΓL₁(𝔽₉)	18	8+	C2xAGammaL(1,9)	288,1027
C₂×S₃×S₄	Direct product of C₂, S₃ and S₄; = Aut(S₃×SL₂(𝔽₃))	18	6+	C2xS3xS4	288,1028
C₂×A₄²	Direct product of C₂, A₄ and A₄	18	9+	C2xA4^2	288,1029

Groups of order 324

		d	ρ	Label	ID
C₉²⋊C₄	The semidirect product of C₉² and C₄ acting faithfully	18	4+	C9^2:C4	324,35
D₉²	Direct product of D₉ and D₉	18	4+	D9^2	324,36
C₃²⋊D₁₈	The semidirect product of C₃² and D₁₈ acting via D₁₈/C₃=D₆	18	12+	C3^2:D18	324,37
C₃³⋊₂A₄	1^st semidirect product of C₃³ and A₄ acting via A₄/C₂²=C₃	18	3	C3^3:2A4	324,60
C₂×C₃≀S₃	Direct product of C₂ and C₃≀S₃	18	3	C2xC3wrS3	324,68
C₂×C₃³⋊C₆	Direct product of C₂ and C₃³⋊C₆	18	6+	C2xC3^3:C6	324,69
C₂×C₃³⋊S₃	Direct product of C₂ and C₃³⋊S₃	18	6+	C2xC3^3:S3	324,77
He₃⋊₄Dic₃	The semidirect product of He₃ and Dic₃ acting via Dic₃/C₃=C₄	18	6	He3:4Dic3	324,113
S₃×C₃²⋊C₆	Direct product of S₃ and C₃²⋊C₆	18	12+	S3xC3^2:C6	324,116
C₃×C₃²⋊D₆	Direct product of C₃ and C₃²⋊D₆	18	6	C3xC3^2:D6	324,117
S₃×C₉⋊C₆	Direct product of S₃ and C₉⋊C₆	18	12+	S3xC9:C6	324,118
He₃⋊₅D₆	1^st semidirect product of He₃ and D₆ acting via D₆/C₃=C₂²	18	12+	He3:5D6	324,121
S₃×He₃⋊C₂	Direct product of S₃ and He₃⋊C₂	18	6	S3xHe3:C2	324,122
C₃⁴⋊₄C₄	4^th semidirect product of C₃⁴ and C₄ acting faithfully	18		C3^4:4C4	324,164
C₃⋊S₃²	Direct product of C₃⋊S₃ and C₃⋊S₃	18		C3:S3^2	324,169

Groups of order 432

		d	ρ	Label	ID
C₆²⋊₅D₆	5^th semidirect product of C₆² and D₆ acting faithfully	18	6+	C6^2:5D6	432,523
C₂×C₃².S₄	Direct product of C₂ and C₃².S₄	18	6+	C2xC3^2.S4	432,533
C₂×C₆²⋊S₃	Direct product of C₂ and C₆²⋊S₃	18	6+	C2xC6^2:S3	432,535
C₂×C₃²⋊S₄	Direct product of C₂ and C₃²⋊S₄	18	3	C2xC3^2:S4	432,538
C₂×C₆²⋊C₆	Direct product of C₂ and C₆²⋊C₆	18	6+	C2xC6^2:C6	432,542
C₂×ASL₂(𝔽₃)	Direct product of C₂ and ASL₂(𝔽₃)	18	8+	C2xASL(2,3)	432,735

Groups of order 486

		d	ρ	Label	ID
C₃²⋊C₉.S₃	1^st non-split extension by C₃²⋊C₉ of S₃ acting faithfully	18	6	C3^2:C9.S3	486,5
C₃²⋊C₉⋊C₆	1^st semidirect product of C₃²⋊C₉ and C₆ acting faithfully	18	6	C3^2:C9:C6	486,6
C₃²⋊C₉⋊S₃	1^st semidirect product of C₃²⋊C₉ and S₃ acting faithfully	18	6	C3^2:C9:S3	486,7
C₃³⋊₁C₁₈	1^st semidirect product of C₃³ and C₁₈ acting via C₁₈/C₃=C₆	18	6	C3^3:1C18	486,18
C₃³⋊₁D₉	1^st semidirect product of C₃³ and D₉ acting via D₉/C₃=S₃	18	6	C3^3:1D9	486,19
C₃⁴⋊C₆	1^st semidirect product of C₃⁴ and C₆ acting faithfully	18	6	C3^4:C6	486,102
C₃⁴.C₆	4^th non-split extension by C₃⁴ of C₆ acting faithfully	18	6	C3^4.C6	486,104
C₉²⋊₈C₆	8^th semidirect product of C₉² and C₆ acting faithfully	18	6	C9^2:8C6	486,110
C₃×C₃³⋊C₆	Direct product of C₃ and C₃³⋊C₆	18	6	C3xC3^3:C6	486,116
S₃×C₃≀C₃	Direct product of S₃ and C₃≀C₃	18	6	S3xC3wrC3	486,117
C₃⁴⋊₃S₃	3^rd semidirect product of C₃⁴ and S₃ acting faithfully	18	6	C3^4:3S3	486,145
C₃⁴.₇S₃	7^th non-split extension by C₃⁴ of S₃ acting faithfully	18	6	C3^4.7S3	486,147
C₉²⋊₆S₃	6^th semidirect product of C₉² and S₃ acting faithfully	18	6	C9^2:6S3	486,153
C₃×C₃³⋊S₃	Direct product of C₃ and C₃³⋊S₃	18	6	C3xC3^3:S3	486,165
C₃⁴⋊₅S₃	5^th semidirect product of C₃⁴ and S₃ acting faithfully	18	6	C3^4:5S3	486,166

On 19 points

Groups of order 19

		d	ρ	Label	ID
C₁₉	Cyclic group	19	1	C19	19,1

Groups of order 38

		d	ρ	Label	ID
D₁₉	Dihedral group	19	2+	D19	38,1

Groups of order 57

		d	ρ	Label	ID
C₁₉⋊C₃	The semidirect product of C₁₉ and C₃ acting faithfully	19	3	C19:C3	57,1

Groups of order 114

		d	ρ	Label	ID
C₁₉⋊C₆	The semidirect product of C₁₉ and C₆ acting faithfully	19	6+	C19:C6	114,1

Groups of order 171

		d	ρ	Label	ID
C₁₉⋊C₉	The semidirect product of C₁₉ and C₉ acting faithfully	19	9	C19:C9	171,3

Groups of order 342

		d	ρ	Label	ID
F₁₉	Frobenius group; = C₁₉ ⋊C₁₈ = AGL₁(𝔽₁₉) = Aut(D₁₉) = Hol(C₁₉)	19	18+	F19	342,7

On 20 points

Groups of order 20

		d	ρ	Label	ID
Dic₅	Dicyclic group; = C₅ ⋊₂ C₄	20	2-	Dic5	20,1
C₂₀	Cyclic group	20	1	C20	20,2
C₂×C₁₀	Abelian group of type [2,10]	20		C2xC10	20,5

Groups of order 40

		d	ρ	Label	ID
C₄×D₅	Direct product of C₄ and D₅	20	2	C4xD5	40,5
D₂₀	Dihedral group	20	2+	D20	40,6
C₅⋊D₄	The semidirect product of C₅ and D₄ acting via D₄/C₂²=C₂	20	2	C5:D4	40,8
C₅×D₄	Direct product of C₅ and D₄	20	2	C5xD4	40,10
C₂²×D₅	Direct product of C₂² and D₅	20		C2^2xD5	40,13

Groups of order 60

		d	ρ	Label	ID
C₅×A₄	Direct product of C₅ and A₄	20	3	C5xA4	60,9

Groups of order 80

		d	ρ	Label	ID
C₄×F₅	Direct product of C₄ and F₅	20	4	C4xF5	80,30
C₄⋊F₅	The semidirect product of C₄ and F₅ acting via F₅/D₅=C₂	20	4	C4:F5	80,31
C₂²⋊F₅	The semidirect product of C₂² and F₅ acting via F₅/D₅=C₂	20	4+	C2^2:F5	80,34
D₄×D₅	Direct product of D₄ and D₅	20	4+	D4xD5	80,39
C₂²×F₅	Direct product of C₂² and F₅	20		C2^2xF5	80,50

Groups of order 100

		d	ρ	Label	ID
C₅×Dic₅	Direct product of C₅ and Dic₅	20	2	C5xDic5	100,6
C₅×F₅	Direct product of C₅ and F₅	20	4	C5xF5	100,9
D₅.D₅	The non-split extension by D₅ of D₅ acting via D₅/C₅=C₂	20	4	D5.D5	100,10
D₅×C₁₀	Direct product of C₁₀ and D₅	20	2	D5xC10	100,14

Groups of order 120

		d	ρ	Label	ID
C₅×S₄	Direct product of C₅ and S₄	20	3	C5xS4	120,37
C₅⋊S₄	The semidirect product of C₅ and S₄ acting via S₄/A₄=C₂	20	6+	C5:S4	120,38
D₅×A₄	Direct product of D₅ and A₄	20	6+	D5xA4	120,39

Groups of order 160

		d	ρ	Label	ID
D₄×F₅	Direct product of D₄ and F₅; = Aut(D₂₀) = Hol(C₂₀)	20	8+	D4xF5	160,207

Groups of order 200

		d	ρ	Label	ID
Dic₅⋊₂D₅	The semidirect product of Dic₅ and D₅ acting through Inn(Dic₅)	20	4+	Dic5:2D5	200,23
C₅⋊D₂₀	The semidirect product of C₅ and D₂₀ acting via D₂₀/D₁₀=C₂	20	4+	C5:D20	200,25
C₅×C₅⋊D₄	Direct product of C₅ and C₅⋊D₄	20	2	C5xC5:D4	200,31
D₅×F₅	Direct product of D₅ and F₅	20	8+	D5xF5	200,41
C₂×C₅²⋊C₄	Direct product of C₂ and C₅²⋊C₄	20	4+	C2xC5^2:C4	200,48
C₂×D₅²	Direct product of C₂, D₅ and D₅	20	4+	C2xD5^2	200,49

Groups of order 240

		d	ρ	Label	ID
C₄×A₅	Direct product of C₄ and A₅	20	3	C4xA5	240,92
C₂²×A₅	Direct product of C₂² and A₅	20		C2^2xA5	240,190
A₄⋊F₅	The semidirect product of A₄ and F₅ acting via F₅/D₅=C₂	20	12+	A4:F5	240,192
A₄×F₅	Direct product of A₄ and F₅	20	12+	A4xF5	240,193
D₅×S₄	Direct product of D₅ and S₄	20	6+	D5xS4	240,194

Groups of order 320

		d	ρ	Label	ID
C₂⁵.D₅	The non-split extension by C₂⁵ of D₅ acting faithfully	20	5	C2^5.D5	320,1583
C₄×C₂⁴⋊C₅	Direct product of C₄ and C₂⁴⋊C₅	20	5	C4xC2^4:C5	320,1584
C₂²×C₂⁴⋊C₅	Direct product of C₂² and C₂⁴⋊C₅	20		C2^2xC2^4:C5	320,1637

Groups of order 400

		d	ρ	Label	ID
C₅²⋊₃C₄²	2^nd semidirect product of C₅² and C₄² acting via C₄²/C₂=C₂×C₄	20	8+	C5^2:3C4^2	400,124
D₁₀⋊F₅	2^nd semidirect product of D₁₀ and F₅ acting via F₅/D₅=C₂	20	8+	D10:F5	400,125
Dic₅⋊F₅	3^rd semidirect product of Dic₅ and F₅ acting via F₅/D₅=C₂	20	8+	Dic5:F5	400,126
D₅²⋊C₄	1^st semidirect product of D₅² and C₄ acting via C₄/C₂=C₂	20	4+	D5^2:C4	400,129
C₂.D₅≀C₂	2^nd central extension by C₂ of D₅≀C₂	20	4	C2.D5wrC2	400,130
(C₅×C₁₀).Q₈	The non-split extension by C₅×C₁₀ of Q₈ acting faithfully	20	8+	(C5xC10).Q8	400,134
C₁₀²⋊₄C₄	4^th semidirect product of C₁₀² and C₄ acting faithfully	20	4+	C10^2:4C4	400,162
D₁₀⋊D₁₀	3^rd semidirect product of D₁₀ and D₁₀ acting via D₁₀/D₅=C₂	20	4+	D10:D10	400,180
F₅²	Direct product of F₅ and F₅; = Hol(F₅)	20	16+	F5^2	400,205
C₂×C₅²⋊C₈	Direct product of C₂ and C₅²⋊C₈	20	8+	C2xC5^2:C8	400,208
C₂×D₅⋊F₅	Direct product of C₂ and D₅⋊F₅	20	8+	C2xD5:F5	400,210
C₂×D₅≀C₂	Direct product of C₂ and D₅≀C₂	20	4+	C2xD5wrC2	400,211
C₂×C₅²⋊Q₈	Direct product of C₂ and C₅²⋊Q₈	20	8+	C2xC5^2:Q8	400,212

Groups of order 480

		d	ρ	Label	ID
C₄×S₅	Direct product of C₄ and S₅; = CO₃(𝔽₅)	20	4	C4xS5	480,943
C₄⋊S₅	The semidirect product of C₄ and S₅ acting via S₅/A₅=C₂	20	6	C4:S5	480,944
C₂²⋊S₅	The semidirect product of C₂² and S₅ acting via S₅/A₅=C₂	20	6+	C2^2:S5	480,951
D₄×A₅	Direct product of D₄ and A₅	20	6+	D4xA5	480,956
C₂²×S₅	Direct product of C₂² and S₅	20		C2^2xS5	480,1186
F₅×S₄	Direct product of F₅ and S₄; = Hol(C₂×C₁₀)	20	12+	F5xS4	480,1189

Groups of order 500

		d	ρ	Label	ID
C₅×D₅.D₅	Direct product of C₅ and D₅.D₅	20	4	C5xD5.D5	500,42
C₅×C₅²⋊C₄	Direct product of C₅ and C₅²⋊C₄	20	4	C5xC5^2:C4	500,44
C₅³⋊₆C₄	6^th semidirect product of C₅³ and C₄ acting faithfully	20	4	C5^3:6C4	500,46
C₅×D₅²	Direct product of C₅, D₅ and D₅	20	4	C5xD5^2	500,50
C₅²⋊₅D₁₀	2^nd semidirect product of C₅² and D₁₀ acting via D₁₀/C₅=C₂²	20	4	C5^2:5D10	500,52

On 21 points

Groups of order 21

		d	ρ	Label	ID
C₂₁	Cyclic group	21	1	C21	21,2

Groups of order 42

		d	ρ	Label	ID
S₃×C₇	Direct product of C₇ and S₃	21	2	S3xC7	42,3
C₃×D₇	Direct product of C₃ and D₇	21	2	C3xD7	42,4
D₂₁	Dihedral group	21	2+	D21	42,5

Groups of order 63

		d	ρ	Label	ID
C₃×C₇⋊C₃	Direct product of C₃ and C₇⋊C₃	21	3	C3xC7:C3	63,3

Groups of order 84

		d	ρ	Label	ID
S₃×D₇	Direct product of S₃ and D₇	21	4+	S3xD7	84,8

Groups of order 126

		d	ρ	Label	ID
C₃×F₇	Direct product of C₃ and F₇	21	6	C3xF7	126,7
S₃×C₇⋊C₃	Direct product of S₃ and C₇⋊C₃	21	6	S3xC7:C3	126,8
C₃⋊F₇	The semidirect product of C₃ and F₇ acting via F₇/C₇⋊C₃=C₂	21	6+	C3:F7	126,9

Groups of order 147

		d	ρ	Label	ID
C₇×C₇⋊C₃	Direct product of C₇ and C₇⋊C₃	21	3	C7xC7:C3	147,3
C₇²⋊₃C₃	3^rd semidirect product of C₇² and C₃ acting faithfully	21	3	C7^2:3C3	147,5

Groups of order 252

		d	ρ	Label	ID
S₃×F₇	Direct product of S₃ and F₇; = Aut(D₂₁) = Hol(C₂₁)	21	12+	S3xF7	252,26

Groups of order 294

		d	ρ	Label	ID
C₇⋊₅F₇	The semidirect product of C₇ and F₇ acting via F₇/C₇⋊C₃=C₂	21	6+	C7:5F7	294,10
C₇²⋊C₆	7^th semidirect product of C₇² and C₆ acting faithfully	21	6+	C7^2:C6	294,14

Groups of order 441

		d	ρ	Label	ID
C₇⋊C₃²	Direct product of C₇⋊C₃ and C₇⋊C₃	21	9	C7:C3^2	441,9

On 22 points

Groups of order 22

		d	ρ	Label	ID
C₂₂	Cyclic group	22	1	C22	22,2

Groups of order 44

		d	ρ	Label	ID
D₂₂	Dihedral group; = C₂×D₁₁	22	2+	D22	44,3

Groups of order 110

		d	ρ	Label	ID
C₂×C₁₁⋊C₅	Direct product of C₂ and C₁₁⋊C₅	22	5	C2xC11:C5	110,2

Groups of order 220

		d	ρ	Label	ID
C₂×F₁₁	Direct product of C₂ and F₁₁; = Aut(D₂₂) = Hol(C₂₂)	22	10+	C2xF11	220,7

Groups of order 242

		d	ρ	Label	ID
C₁₁×D₁₁	Direct product of C₁₁ and D₁₁; = AΣL₁(𝔽₁₂₁)	22	2	C11xD11	242,3

Groups of order 484

		d	ρ	Label	ID
C₁₁²⋊C₄	The semidirect product of C₁₁² and C₄ acting faithfully	22	4+	C11^2:C4	484,8
D₁₁²	Direct product of D₁₁ and D₁₁	22	4+	D11^2	484,9

On 23 points

Groups of order 23

		d	ρ	Label	ID
C₂₃	Cyclic group	23	1	C23	23,1

Groups of order 46

		d	ρ	Label	ID
D₂₃	Dihedral group	23	2+	D23	46,1

Groups of order 253

		d	ρ	Label	ID
C₂₃⋊C₁₁	The semidirect product of C₂₃ and C₁₁ acting faithfully	23	11	C23:C11	253,1

On 24 points

Groups of order 24

		d	ρ	Label	ID
C₃⋊C₈	The semidirect product of C₃ and C₈ acting via C₈/C₄=C₂	24	2	C3:C8	24,1
C₂₄	Cyclic group	24	1	C24	24,2
Dic₆	Dicyclic group; = C₃ ⋊Q₈	24	2-	Dic6	24,4
C₂×Dic₃	Direct product of C₂ and Dic₃	24		C2xDic3	24,7
C₂×C₁₂	Abelian group of type [2,12]	24		C2xC12	24,9
C₃×Q₈	Direct product of C₃ and Q₈	24	2	C3xQ8	24,11
C₂²×C₆	Abelian group of type [2,2,6]	24		C2^2xC6	24,15

Groups of order 48

		d	ρ	Label	ID
S₃×C₈	Direct product of C₈ and S₃	24	2	S3xC8	48,4
C₈⋊S₃	3^rd semidirect product of C₈ and S₃ acting via S₃/C₃=C₂	24	2	C8:S3	48,5
C₂₄⋊C₂	2^nd semidirect product of C₂₄ and C₂ acting faithfully	24	2	C24:C2	48,6
D₂₄	Dihedral group	24	2+	D24	48,7
C₄.Dic₃	The non-split extension by C₄ of Dic₃ acting via Dic₃/C₆=C₂	24	2	C4.Dic3	48,10
D₆⋊C₄	The semidirect product of D₆ and C₄ acting via C₄/C₂=C₂	24		D6:C4	48,14
D₄⋊S₃	The semidirect product of D₄ and S₃ acting via S₃/C₃=C₂	24	4+	D4:S3	48,15
D₄.S₃	The non-split extension by D₄ of S₃ acting via S₃/C₃=C₂	24	4-	D4.S3	48,16
Q₈⋊₂S₃	The semidirect product of Q₈ and S₃ acting via S₃/C₃=C₂	24	4+	Q8:2S3	48,17
C₆.D₄	7^th non-split extension by C₆ of D₄ acting via D₄/C₂²=C₂	24		C6.D4	48,19
C₃×C₂²⋊C₄	Direct product of C₃ and C₂²⋊C₄	24		C3xC2^2:C4	48,21
C₃×M₄(2)	Direct product of C₃ and M₄(2)	24	2	C3xM4(2)	48,24
C₃×D₈	Direct product of C₃ and D₈	24	2	C3xD8	48,25
C₃×SD₁₆	Direct product of C₃ and SD₁₆	24	2	C3xSD16	48,26
S₃×C₂×C₄	Direct product of C₂×C₄ and S₃	24		S3xC2xC4	48,35
C₂×D₁₂	Direct product of C₂ and D₁₂	24		C2xD12	48,36
C₄○D₁₂	Central product of C₄ and D₁₂	24	2	C4oD12	48,37
D₄⋊₂S₃	The semidirect product of D₄ and S₃ acting through Inn(D₄)	24	4-	D4:2S3	48,39
S₃×Q₈	Direct product of S₃ and Q₈	24	4-	S3xQ8	48,40
Q₈⋊₃S₃	The semidirect product of Q₈ and S₃ acting through Inn(Q₈)	24	4+	Q8:3S3	48,41
C₂×C₃⋊D₄	Direct product of C₂ and C₃⋊D₄	24		C2xC3:D4	48,43
C₆×D₄	Direct product of C₆ and D₄	24		C6xD4	48,45
C₃×C₄○D₄	Direct product of C₃ and C₄○D₄	24	2	C3xC4oD4	48,47
S₃×C₂³	Direct product of C₂³ and S₃	24		S3xC2^3	48,51

Groups of order 72

		d	ρ	Label	ID
C₃×C₃⋊C₈	Direct product of C₃ and C₃⋊C₈	24	2	C3xC3:C8	72,12
C₃²⋊₂C₈	The semidirect product of C₃² and C₈ acting via C₈/C₂=C₄	24	4-	C3^2:2C8	72,19
S₃×Dic₃	Direct product of S₃ and Dic₃	24	4-	S3xDic3	72,20
D₆⋊S₃	1^st semidirect product of D₆ and S₃ acting via S₃/C₃=C₂	24	4-	D6:S3	72,22
C₃²⋊₂Q₈	The semidirect product of C₃² and Q₈ acting via Q₈/C₂=C₂²	24	4-	C3^2:2Q8	72,24
C₃×SL₂(𝔽₃)	Direct product of C₃ and SL₂(𝔽₃)	24	2	C3xSL(2,3)	72,25
C₃×Dic₆	Direct product of C₃ and Dic₆	24	2	C3xDic6	72,26
S₃×C₁₂	Direct product of C₁₂ and S₃	24	2	S3xC12	72,27
C₃×D₁₂	Direct product of C₃ and D₁₂	24	2	C3xD12	72,28
C₆×Dic₃	Direct product of C₆ and Dic₃	24		C6xDic3	72,29
S₃×C₂×C₆	Direct product of C₂×C₆ and S₃	24		S3xC2xC6	72,48

Groups of order 96

		d	ρ	Label	ID
C₄²⋊₄S₃	3^rd semidirect product of C₄² and S₃ acting via S₃/C₃=C₂	24	2	C4^2:4S3	96,12
C₂³.₆D₆	1^st non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	24	4	C2^3.6D6	96,13
C₁₂.₄₆D₄	3^rd non-split extension by C₁₂ of D₄ acting via D₄/C₂²=C₂	24	4+	C12.46D4	96,30
D₁₂⋊C₄	4^th semidirect product of D₁₂ and C₄ acting via C₄/C₂=C₂	24	4	D12:C4	96,32
C₁₂.D₄	8^th non-split extension by C₁₂ of D₄ acting via D₄/C₂=C₂²	24	4	C12.D4	96,40
C₂³.₇D₆	2^nd non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	24	4	C2^3.7D6	96,41
Q₈⋊₃Dic₃	2^nd semidirect product of Q₈ and Dic₃ acting via Dic₃/C₆=C₂	24	4	Q8:3Dic3	96,44
C₃×C₂³⋊C₄	Direct product of C₃ and C₂³⋊C₄	24	4	C3xC2^3:C4	96,49
C₃×C₄.D₄	Direct product of C₃ and C₄.D₄	24	4	C3xC4.D4	96,50
C₃×C₄≀C₂	Direct product of C₃ and C₄≀C₂	24	2	C3xC4wrC2	96,54
A₄⋊C₈	The semidirect product of A₄ and C₈ acting via C₈/C₄=C₂	24	3	A4:C8	96,65
U₂(𝔽₃)	Unitary group on 𝔽₃²; = SL₂(𝔽₃)⋊₂ C₄	24	2	U(2,3)	96,67
C₈×A₄	Direct product of C₈ and A₄	24	3	C8xA4	96,73
S₃×C₂²⋊C₄	Direct product of S₃ and C₂²⋊C₄	24		S3xC2^2:C4	96,87
D₆⋊D₄	1^st semidirect product of D₆ and D₄ acting via D₄/C₂²=C₂	24		D6:D4	96,89
S₃×M₄(2)	Direct product of S₃ and M₄(2)	24	4	S3xM4(2)	96,113
C₈⋊D₆	1^st semidirect product of C₈ and D₆ acting via D₆/C₃=C₂²	24	4+	C8:D6	96,115
S₃×D₈	Direct product of S₃ and D₈	24	4+	S3xD8	96,117
D₈⋊S₃	2^nd semidirect product of D₈ and S₃ acting via S₃/C₃=C₂	24	4	D8:S3	96,118
S₃×SD₁₆	Direct product of S₃ and SD₁₆	24	4	S3xSD16	96,120
Q₈⋊₃D₆	2^nd semidirect product of Q₈ and D₆ acting via D₆/S₃=C₂	24	4+	Q8:3D6	96,121
D₁₂⋊₆C₂²	4^th semidirect product of D₁₂ and C₂² acting via C₂²/C₂=C₂	24	4	D12:6C2^2	96,139
C₂³⋊₂D₆	1^st semidirect product of C₂³ and D₆ acting via D₆/C₃=C₂²	24		C2^3:2D6	96,144
D₄⋊D₆	2^nd semidirect product of D₄ and D₆ acting via D₆/C₆=C₂	24	4+	D4:D6	96,156
C₂⁴⋊₄S₃	1^st semidirect product of C₂⁴ and S₃ acting via S₃/C₃=C₂	24		C2^4:4S3	96,160
C₃×C₂²≀C₂	Direct product of C₃ and C₂²≀C₂	24		C3xC2^2wrC2	96,167
C₃×C₈⋊C₂²	Direct product of C₃ and C₈⋊C₂²	24	4	C3xC8:C2^2	96,183
A₄⋊Q₈	The semidirect product of A₄ and Q₈ acting via Q₈/C₄=C₂	24	6-	A4:Q8	96,185
C₂×A₄⋊C₄	Direct product of C₂ and A₄⋊C₄	24		C2xA4:C4	96,194
C₂×C₄×A₄	Direct product of C₂×C₄ and A₄	24		C2xC4xA4	96,196
Q₈×A₄	Direct product of Q₈ and A₄	24	6-	Q8xA4	96,199
Q₈.A₄	The non-split extension by Q₈ of A₄ acting through Inn(Q₈)	24	4+	Q8.A4	96,201
Q₈⋊A₄	1^st semidirect product of Q₈ and A₄ acting via A₄/C₂²=C₃	24	6-	Q8:A4	96,203
C₂×S₃×D₄	Direct product of C₂, S₃ and D₄	24		C2xS3xD4	96,209
D₄⋊₆D₆	2^nd semidirect product of D₄ and D₆ acting through Inn(D₄)	24	4	D4:6D6	96,211
S₃×C₄○D₄	Direct product of S₃ and C₄○D₄	24	4	S3xC4oD4	96,215
D₄○D₁₂	Central product of D₄ and D₁₂	24	4+	D4oD12	96,216
C₃×2₊¹⁺⁴	Direct product of C₃ and 2₊¹⁺⁴	24	4	C3xES+(2,2)	96,224
C₂³×A₄	Direct product of C₂³ and A₄	24		C2^3xA4	96,228

Groups of order 120

		d	ρ	Label	ID
SL₂(𝔽₅)	Special linear group on 𝔽₅²; = C₂ .A₅ = 2I = <2,3,5>	24	2-	SL(2,5)	120,5

Groups of order 144

		d	ρ	Label	ID
C₁₂.₂₉D₆	3^rd non-split extension by C₁₂ of D₆ acting via D₆/S₃=C₂	24	4	C12.29D6	144,53
C₁₂.₃₁D₆	5^th non-split extension by C₁₂ of D₆ acting via D₆/S₃=C₂	24	4	C12.31D6	144,55
C₃⋊D₂₄	The semidirect product of C₃ and D₂₄ acting via D₂₄/D₁₂=C₂	24	4+	C3:D24	144,57
C₃²⋊₅SD₁₆	3^rd semidirect product of C₃² and SD₁₆ acting via SD₁₆/C₄=C₂²	24	4+	C3^2:5SD16	144,60
C₆.D₁₂	6^th non-split extension by C₆ of D₁₂ acting via D₁₂/D₆=C₂	24		C6.D12	144,65
C₃×C₄.Dic₃	Direct product of C₃ and C₄.Dic₃	24	2	C3xC4.Dic3	144,75
C₃×D₄⋊S₃	Direct product of C₃ and D₄⋊S₃	24	4	C3xD4:S3	144,80
C₃×D₄.S₃	Direct product of C₃ and D₄.S₃	24	4	C3xD4.S3	144,81
C₃×C₆.D₄	Direct product of C₃ and C₆.D₄	24		C3xC6.D4	144,84
C₃⋊S₃.Q₈	The non-split extension by C₃⋊S₃ of Q₈ acting via Q₈/C₂=C₂²	24	4	C3:S3.Q8	144,116
C₃²⋊D₈	The semidirect product of C₃² and D₈ acting via D₈/C₂=D₄	24	4	C3^2:D8	144,117
C₃²⋊₂SD₁₆	The semidirect product of C₃² and SD₁₆ acting via SD₁₆/C₂=D₄	24	4-	C3^2:2SD16	144,118
C₂.PSU₃(𝔽₂)	The central extension by C₂ of PSU₃(𝔽₂)	24	8+	C2.PSU(3,2)	144,120
C₃×GL₂(𝔽₃)	Direct product of C₃ and GL₂(𝔽₃)	24	2	C3xGL(2,3)	144,122
C₆.₆S₄	6^th non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	24	4+	C6.6S4	144,125
S₃×SL₂(𝔽₃)	Direct product of S₃ and SL₂(𝔽₃); = SL₂(ℤ/6ℤ)	24	4-	S3xSL(2,3)	144,128
C₃⋊S₃⋊₃C₈	2^nd semidirect product of C₃⋊S₃ and C₈ acting via C₈/C₄=C₂	24	4	C3:S3:3C8	144,130
C₃²⋊M₄(2)	The semidirect product of C₃² and M₄(2) acting via M₄(2)/C₄=C₄	24	4	C3^2:M4(2)	144,131
C₄×C₃²⋊C₄	Direct product of C₄ and C₃²⋊C₄	24	4	C4xC3^2:C4	144,132
C₄⋊(C₃²⋊C₄)	The semidirect product of C₄ and C₃²⋊C₄ acting via C₃²⋊C₄/C₃⋊S₃=C₂	24	4	C4:(C3^2:C4)	144,133
C₆².C₄	2^nd non-split extension by C₆² of C₄ acting faithfully	24	4-	C6^2.C4	144,135
D₁₂⋊S₃	3^rd semidirect product of D₁₂ and S₃ acting via S₃/C₃=C₂	24	4	D12:S3	144,139
Dic₃.D₆	2^nd non-split extension by Dic₃ of D₆ acting via D₆/S₃=C₂	24	4	Dic3.D6	144,140
D₆.D₆	1^st non-split extension by D₆ of D₆ acting via D₆/C₆=C₂	24	4	D6.D6	144,141
D₆.₆D₆	2^nd non-split extension by D₆ of D₆ acting via D₆/C₆=C₂	24	4+	D6.6D6	144,142
C₄×S₃²	Direct product of C₄, S₃ and S₃	24	4	C4xS3^2	144,143
S₃×D₁₂	Direct product of S₃ and D₁₂	24	4+	S3xD12	144,144
D₆⋊D₆	2^nd semidirect product of D₆ and D₆ acting via D₆/S₃=C₂	24	4	D6:D6	144,145
D₆.₃D₆	3^rd non-split extension by D₆ of D₆ acting via D₆/S₃=C₂	24	4	D6.3D6	144,147
D₆.₄D₆	4^th non-split extension by D₆ of D₆ acting via D₆/S₃=C₂	24	4-	D6.4D6	144,148
C₂×C₆.D₆	Direct product of C₂ and C₆.D₆	24		C2xC6.D6	144,149
C₂×C₃⋊D₁₂	Direct product of C₂ and C₃⋊D₁₂	24		C2xC3:D12	144,151
S₃×C₃⋊D₄	Direct product of S₃ and C₃⋊D₄	24	4	S3xC3:D4	144,153
C₃×C₄○D₁₂	Direct product of C₃ and C₄○D₁₂	24	2	C3xC4oD12	144,161
C₃×S₃×D₄	Direct product of C₃, S₃ and D₄	24	4	C3xS3xD4	144,162
C₃×D₄⋊₂S₃	Direct product of C₃ and D₄⋊₂S₃	24	4	C3xD4:2S3	144,163
C₆×C₃⋊D₄	Direct product of C₆ and C₃⋊D₄	24		C6xC3:D4	144,167
C₂²×C₃²⋊C₄	Direct product of C₂² and C₃²⋊C₄	24		C2^2xC3^2:C4	144,191
C₂²×S₃²	Direct product of C₂², S₃ and S₃	24		C2^2xS3^2	144,192

Groups of order 168

		d	ρ	Label	ID
C₃×F₈	Direct product of C₃ and F₈	24	7	C3xF8	168,44

Groups of order 192

		d	ρ	Label	ID
C₈²⋊C₃	The semidirect product of C₈² and C₃ acting faithfully	24	3	C8^2:C3	192,3
C₃⋊C₂≀C₄	The semidirect product of C₃ and C₂≀C₄ acting via C₂≀C₄/C₂³⋊C₄=C₂	24	8+	C3:C2wrC4	192,30
C₂³.₂D₁₂	2^nd non-split extension by C₂³ of D₁₂ acting via D₁₂/C₃=D₄	24	8+	C2^3.2D12	192,33
C₂³.₃D₁₂	3^rd non-split extension by C₂³ of D₁₂ acting via D₁₂/C₃=D₄	24	8+	C2^3.3D12	192,34
C₂⁴⋊₅Dic₃	1^st semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₃=C₄	24	4	C2^4:5Dic3	192,95
C₄²⋊₅Dic₃	3^rd semidirect product of C₄² and Dic₃ acting via Dic₃/C₃=C₄	24	4	C4^2:5Dic3	192,104
C₃×C₂≀C₄	Direct product of C₃ and C₂≀C₄	24	4	C3xC2wrC4	192,157
C₃×C₄²⋊C₄	Direct product of C₃ and C₄²⋊C₄	24	4	C3xC4^2:C4	192,159
C₂³.₇S₄	1^st non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	24	6	C2^3.7S4	192,180
C₂³.₈S₄	2^nd non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	24	6+	C2^3.8S4	192,181
C₂×C₂³.₃A₄	Direct product of C₂ and C₂³.₃A₄	24		C2xC2^3.3A4	192,189
C₄²⋊₄C₄⋊C₃	The semidirect product of C₄²⋊₄C₄ and C₃ acting faithfully	24	6	C4^2:4C4:C3	192,190
C₄²⋊C₁₂	1^st semidirect product of C₄² and C₁₂ acting via C₁₂/C₂=C₆	24	6	C4^2:C12	192,192
C₄²⋊₂C₁₂	2^nd semidirect product of C₄² and C₁₂ acting via C₁₂/C₂=C₆	24	6-	C4^2:2C12	192,193
C₂⁴.A₄	1^st non-split extension by C₂⁴ of A₄ acting faithfully	24	6	C2^4.A4	192,195
(C₂²×C₄).A₄	4^th non-split extension by C₂²×C₄ of A₄ acting faithfully	24	6-	(C2^2xC4).A4	192,196
C₂⁴.₃A₄	3^rd non-split extension by C₂⁴ of A₄ acting faithfully	24	6	C2^4.3A4	192,198
C₂³.₁₉(C₂×A₄)	12^nd non-split extension by C₂³ of C₂×A₄ acting via C₂×A₄/C₂³=C₃	24	6	C2^3.19(C2xA4)	192,199
C₂³⋊D₁₂	The semidirect product of C₂³ and D₁₂ acting via D₁₂/C₃=D₄	24	8+	C2^3:D12	192,300
S₃×C₂³⋊C₄	Direct product of S₃ and C₂³⋊C₄	24	8+	S3xC2^3:C4	192,302
S₃×C₄.D₄	Direct product of S₃ and C₄.D₄	24	8+	S3xC4.D4	192,303
D₁₂⋊₁D₄	1^st semidirect product of D₁₂ and D₄ acting via D₄/C₂=C₂²	24	8+	D12:1D4	192,306
S₃×C₄≀C₂	Direct product of S₃ and C₄≀C₂	24	4	S3xC4wrC2	192,379
Q₈⋊₅D₁₂	3^rd semidirect product of Q₈ and D₁₂ acting via D₁₂/D₆=C₂	24	4+	Q8:5D12	192,381
C₂⁴⋊₆D₆	1^st semidirect product of C₂⁴ and D₆ acting via D₆/C₃=C₂²	24	4	C2^4:6D6	192,591
C₄²⋊₈D₆	6^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	24	4	C4^2:8D6	192,636
D₁₂⋊₁₈D₄	6^th semidirect product of D₁₂ and D₄ acting via D₄/C₂²=C₂	24	8+	D12:18D4	192,757
2₊¹⁺⁴⋊₆S₃	1^st semidirect product of 2₊¹⁺⁴ and S₃ acting via S₃/C₃=C₂	24	8+	ES+(2,2):6S3	192,800
2₊¹⁺⁴⋊₇S₃	2^nd semidirect product of 2₊¹⁺⁴ and S₃ acting via S₃/C₃=C₂	24	8+	ES+(2,2):7S3	192,803
C₃×D₄⋊₄D₄	Direct product of C₃ and D₄⋊₄D₄	24	4	C3xD4:4D4	192,886
C₃×C₂≀C₂²	Direct product of C₃ and C₂≀C₂²	24	4	C3xC2wrC2^2	192,890
C₈×S₄	Direct product of C₈ and S₄	24	3	C8xS4	192,958
C₈⋊S₄	3^rd semidirect product of C₈ and S₄ acting via S₄/A₄=C₂	24	6	C8:S4	192,959
C₈⋊₂S₄	2^nd semidirect product of C₈ and S₄ acting via S₄/A₄=C₂	24	6	C8:2S4	192,960
A₄⋊D₈	The semidirect product of A₄ and D₈ acting via D₈/C₈=C₂	24	6+	A4:D8	192,961
A₄⋊M₄(2)	The semidirect product of A₄ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	24	6	A4:M4(2)	192,968
C₂⁴.₅D₆	4^th non-split extension by C₂⁴ of D₆ acting via D₆/C₂=S₃	24		C2^4.5D6	192,972
A₄⋊SD₁₆	The semidirect product of A₄ and SD₁₆ acting via SD₁₆/D₄=C₂	24	6	A4:SD16	192,973
D₄⋊S₄	The semidirect product of D₄ and S₄ acting via S₄/A₄=C₂	24	6+	D4:S4	192,974
Q₈⋊₃S₄	The semidirect product of Q₈ and S₄ acting via S₄/A₄=C₂	24	6	Q8:3S4	192,976
Q₈.₅S₄	3^rd non-split extension by Q₈ of S₄ acting via S₄/A₄=C₂	24	4+	Q8.5S4	192,988
C₂⁵.S₃	1^st non-split extension by C₂⁵ of S₃ acting faithfully	24		C2^5.S3	192,991
C₂²×C₄²⋊C₃	Direct product of C₂² and C₄²⋊C₃	24		C2^2xC4^2:C3	192,992
A₄×C₂²⋊C₄	Direct product of A₄ and C₂²⋊C₄	24		A4xC2^2:C4	192,994
C₂×C₄²⋊C₆	Direct product of C₂ and C₄²⋊C₆	24	6	C2xC4^2:C6	192,1001
A₄×M₄(2)	Direct product of A₄ and M₄(2)	24	6	A4xM4(2)	192,1011
A₄×D₈	Direct product of A₄ and D₈	24	6+	A4xD8	192,1014
A₄×SD₁₆	Direct product of A₄ and SD₁₆	24	6	A4xSD16	192,1015
C₄²⋊₂A₄	The semidirect product of C₄² and A₄ acting via A₄/C₂²=C₃	24		C4^2:2A4	192,1020
S₃×C₂²≀C₂	Direct product of S₃ and C₂²≀C₂	24		S3xC2^2wrC2	192,1147
S₃×C₈⋊C₂²	Direct product of S₃ and C₈⋊C₂²; = Aut(D₂₄) = Hol(C₂₄)	24	8+	S3xC8:C2^2	192,1331
C₂×C₄×S₄	Direct product of C₂×C₄ and S₄	24		C2xC4xS4	192,1469
C₂×C₄⋊S₄	Direct product of C₂ and C₄⋊S₄	24		C2xC4:S4	192,1470
C₂⁴.₁₀D₆	9^th non-split extension by C₂⁴ of D₆ acting via D₆/C₂=S₃	24	6	C2^4.10D6	192,1471
D₄⋊₂S₄	The semidirect product of D₄ and S₄ acting through Inn(D₄)	24	6	D4:2S4	192,1473
Q₈×S₄	Direct product of Q₈ and S₄	24	6-	Q8xS4	192,1477
Q₈⋊₄S₄	The semidirect product of Q₈ and S₄ acting through Inn(Q₈)	24	6	Q8:4S4	192,1478
C₂×A₄⋊D₄	Direct product of C₂ and A₄⋊D₄	24		C2xA4:D4	192,1488
Q₈⋊S₄	1^st semidirect product of Q₈ and S₄ acting via S₄/C₂²=S₃	24	6	Q8:S4	192,1490
C₂×D₄×A₄	Direct product of C₂, D₄ and A₄	24		C2xD4xA4	192,1497
A₄×C₄○D₄	Direct product of A₄ and C₄○D₄	24	6	A4xC4oD4	192,1501
C₄×C₂²⋊A₄	Direct product of C₄ and C₂²⋊A₄	24		C4xC2^2:A4	192,1505
C₄○D₄⋊A₄	1^st semidirect product of C₄○D₄ and A₄ acting via A₄/C₂²=C₃	24	6	C4oD4:A4	192,1507
S₃×2₊¹⁺⁴	Direct product of S₃ and 2₊¹⁺⁴	24	8+	S3xES+(2,2)	192,1524
C₂³×S₄	Direct product of C₂³ and S₄	24		C2^3xS4	192,1537
C₂⁶⋊C₃	3^rd semidirect product of C₂⁶ and C₃ acting faithfully	24		C2^6:C3	192,1541

Groups of order 216

		d	ρ	Label	ID
C₃×C₃²⋊₂C₈	Direct product of C₃ and C₃²⋊₂C₈	24	4	C3xC3^2:2C8	216,117
C₃³⋊₄C₈	2^nd semidirect product of C₃³ and C₈ acting via C₈/C₂=C₄	24	4	C3^3:4C8	216,118
C₃×S₃×Dic₃	Direct product of C₃, S₃ and Dic₃	24	4	C3xS3xDic3	216,119
C₃×C₆.D₆	Direct product of C₃ and C₆.D₆	24	4	C3xC6.D6	216,120
C₃×D₆⋊S₃	Direct product of C₃ and D₆⋊S₃	24	4	C3xD6:S3	216,121
C₃×C₃⋊D₁₂	Direct product of C₃ and C₃⋊D₁₂	24	4	C3xC3:D12	216,122
C₃×C₃²⋊₂Q₈	Direct product of C₃ and C₃²⋊₂Q₈	24	4	C3xC3^2:2Q8	216,123
C₃³⋊₉(C₂×C₄)	6^th semidirect product of C₃³ and C₂×C₄ acting via C₂×C₄/C₂=C₂²	24	4	C3^3:9(C2xC4)	216,131
C₃³⋊₉D₄	6^th semidirect product of C₃³ and D₄ acting via D₄/C₂=C₂²	24	4	C3^3:9D4	216,132
C₃³⋊₅Q₈	3^rd semidirect product of C₃³ and Q₈ acting via Q₈/C₂=C₂²	24	4	C3^3:5Q8	216,133
C₃×F₉	Direct product of C₃ and F₉	24	8	C3xF9	216,154
C₃⋊F₉	The semidirect product of C₃ and F₉ acting via F₉/C₃²⋊C₄=C₂	24	8	C3:F9	216,155
C₃×PSU₃(𝔽₂)	Direct product of C₃ and PSU₃(𝔽₂)	24	8	C3xPSU(3,2)	216,160
C₃³⋊Q₈	2^nd semidirect product of C₃³ and Q₈ acting faithfully	24	8	C3^3:Q8	216,161
C₃×C₃⋊S₄	Direct product of C₃ and C₃⋊S₄	24	6	C3xC3:S4	216,164
C₃×S₃×A₄	Direct product of C₃, S₃ and A₄	24	6	C3xS3xA4	216,166
C₆×C₃²⋊C₄	Direct product of C₆ and C₃²⋊C₄	24	4	C6xC3^2:C4	216,168
C₂×C₃³⋊C₄	Direct product of C₂ and C₃³⋊C₄	24	4	C2xC3^3:C4	216,169
S₃²×C₆	Direct product of C₆, S₃ and S₃	24	4	S3^2xC6	216,170
C₂×C₃²⋊₄D₆	Direct product of C₂ and C₃²⋊₄D₆	24	4	C2xC3^2:4D6	216,172

Groups of order 240

		d	ρ	Label	ID
C₄.A₅	The central extension by C₄ of A₅	24	2	C4.A5	240,93

Groups of order 288

		d	ρ	Label	ID
C₁₂.₇₀D₁₂	1^st non-split extension by C₁₂ of D₁₂ acting via D₁₂/D₆=C₂	24	4+	C12.70D12	288,207
D₁₂⋊₄Dic₃	4^th semidirect product of D₁₂ and Dic₃ acting via Dic₃/C₆=C₂	24	4	D12:4Dic3	288,216
C₆².₃₁D₄	15^th non-split extension by C₆² of D₄ acting via D₄/C₂=C₂²	24	4	C6^2.31D4	288,228
C₆².₃₂D₄	16^th non-split extension by C₆² of D₄ acting via D₄/C₂=C₂²	24	4	C6^2.32D4	288,229
C₃×C₄²⋊₄S₃	Direct product of C₃ and C₄²⋊₄S₃	24	2	C3xC4^2:4S3	288,239
C₃×C₂³.₆D₆	Direct product of C₃ and C₂³.₆D₆	24	4	C3xC2^3.6D6	288,240
C₃×C₁₂.D₄	Direct product of C₃ and C₁₂.D₄	24	4	C3xC12.D4	288,267
C₃×C₂³.₇D₆	Direct product of C₃ and C₂³.₇D₆	24	4	C3xC2^3.7D6	288,268
S₃²⋊C₈	The semidirect product of S₃² and C₈ acting via C₈/C₄=C₂	24	4	S3^2:C8	288,374
C₄.S₃≀C₂	1^st non-split extension by C₄ of S₃≀C₂ acting via S₃≀C₂/S₃²=C₂	24	4	C4.S3wrC2	288,375
C₃⋊S₃.₂D₈	1^st non-split extension by C₃⋊S₃ of D₈ acting via D₈/C₄=C₂²	24	4	C3:S3.2D8	288,377
C₆².₂D₄	2^nd non-split extension by C₆² of D₄ acting faithfully	24	4+	C6^2.2D4	288,386
Dic₃≀C₂	Wreath product of Dic₃ by C₂	24	4-	Dic3wrC2	288,389
(C₂²×S₃)⋊A₄	The semidirect product of C₂²×S₃ and A₄ acting faithfully	24	6	(C2^2xS3):A4	288,411
(C₆×C₁₂)⋊C₄	1^st semidirect product of C₆×C₁₂ and C₄ acting faithfully	24	4+	(C6xC12):C4	288,422
C₃⋊S₃.₅D₈	The non-split extension by C₃⋊S₃ of D₈ acting via D₈/D₄=C₂	24	8+	C3:S3.5D8	288,430
(C₂×C₆²)⋊C₄	4^th semidirect product of C₂×C₆² and C₄ acting faithfully	24	4	(C2xC6^2):C4	288,434
(C₂×C₆²).C₄	5^th non-split extension by C₂×C₆² of C₄ acting faithfully	24	4	(C2xC6^2).C4	288,436
C₃⋊C₈⋊₂₀D₆	9^th semidirect product of C₃⋊C₈ and D₆ acting via D₆/S₃=C₂	24	4	C3:C8:20D6	288,466
D₁₂⋊₁₈D₆	2^nd semidirect product of D₁₂ and D₆ acting via D₆/C₆=C₂	24	4+	D12:18D6	288,473
D₁₂⋊D₆	4^th semidirect product of D₁₂ and D₆ acting via D₆/C₃=C₂²	24	8+	D12:D6	288,574
Dic₆⋊D₆	4^th semidirect product of Dic₆ and D₆ acting via D₆/C₃=C₂²	24	8+	Dic6:D6	288,578
D₁₂⋊₅D₆	5^th semidirect product of D₁₂ and D₆ acting via D₆/C₃=C₂²	24	8+	D12:5D6	288,585
C₆².₁₁₆C₂³	111^st non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	24		C6^2.116C2^3	288,622
C₆²⋊₈D₄	5^th semidirect product of C₆² and D₄ acting via D₄/C₂=C₂²	24		C6^2:8D4	288,629
C₃×C₂⁴⋊C₆	Direct product of C₃ and C₂⁴⋊C₆	24	6	C3xC2^4:C6	288,634
C₃×D₁₂⋊₆C₂²	Direct product of C₃ and D₁₂⋊₆C₂²	24	4	C3xD12:6C2^2	288,703
C₃×C₂⁴⋊₄S₃	Direct product of C₃ and C₂⁴⋊₄S₃	24		C3xC2^4:4S3	288,724
C₂.AΓL₁(𝔽₉)	1^st central extension by C₂ of AΓL₁(𝔽₉)	24	8+	C2.AGammaL(1,9)	288,841
S₃×GL₂(𝔽₃)	Direct product of S₃ and GL₂(𝔽₃); = GL₂(ℤ/6ℤ)	24	4	S3xGL(2,3)	288,851
A₄×SL₂(𝔽₃)	Direct product of A₄ and SL₂(𝔽₃)	24	6-	A4xSL(2,3)	288,859
Ω₄⁺ (𝔽₃)	Omega group of + type on 𝔽₃⁴; = SL₂(𝔽₃)⋊A₄	24	4+	Omega+(4,3)	288,860
C₂²⋊F₉	The semidirect product of C₂² and F₉ acting via F₉/C₃²⋊C₄=C₂	24	8+	C2^2:F9	288,867
S₃²⋊Q₈	The semidirect product of S₃² and Q₈ acting via Q₈/C₄=C₂	24	4	S3^2:Q8	288,868
C₄.₄S₃≀C₂	4^th non-split extension by C₄ of S₃≀C₂ acting via S₃≀C₂/C₃²⋊C₄=C₂	24	8+	C4.4S3wrC2	288,869
C₃²⋊D₈⋊C₂	3^rd semidirect product of C₃²⋊D₈ and C₂ acting faithfully	24	4	C3^2:D8:C2	288,872
C₃⋊S₃⋊D₈	The semidirect product of C₃⋊S₃ and D₈ acting via D₈/C₄=C₂²	24	8+	C3:S3:D8	288,873
C₃⋊S₃⋊₂SD₁₆	The semidirect product of C₃⋊S₃ and SD₁₆ acting via SD₁₆/C₄=C₂²	24	8+	C3:S3:2SD16	288,875
C₄×S₃≀C₂	Direct product of C₄ and S₃≀C₂	24	4	C4xS3wrC2	288,877
S₃²⋊D₄	The semidirect product of S₃² and D₄ acting via D₄/C₄=C₂	24	4	S3^2:D4	288,878
C₄⋊S₃≀C₂	The semidirect product of C₄ and S₃≀C₂ acting via S₃≀C₂/C₃²⋊C₄=C₂	24	8+	C4:S3wrC2	288,879
C₂×S₃²⋊C₄	Direct product of C₂ and S₃²⋊C₄	24		C2xS3^2:C4	288,880
C₆².₉D₄	9^th non-split extension by C₆² of D₄ acting faithfully	24	4	C6^2.9D4	288,881
C₆².₁₂D₄	12^nd non-split extension by C₆² of D₄ acting faithfully	24	4	C6^2.12D4	288,884
C₆²⋊D₄	2^nd semidirect product of C₆² and D₄ acting faithfully	24	8+	C6^2:D4	288,890
C₆²⋊Q₈	1^st semidirect product of C₆² and Q₈ acting faithfully	24	8+	C6^2:Q8	288,895
C₃⋊S₃⋊M₄(2)	2^nd semidirect product of C₃⋊S₃ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	24	4	C3:S3:M4(2)	288,931
(C₆×C₁₂)⋊₅C₄	5^th semidirect product of C₆×C₁₂ and C₄ acting faithfully	24	4	(C6xC12):5C4	288,934
D₄×C₃²⋊C₄	Direct product of D₄ and C₃²⋊C₄	24	8+	D4xC3^2:C4	288,936
C₂×C₆²⋊C₄	Direct product of C₂ and C₆²⋊C₄	24		C2xC6^2:C4	288,941
D₁₂⋊₂₃D₆	7^th semidirect product of D₁₂ and D₆ acting via D₆/C₆=C₂	24	4	D12:23D6	288,954
D₁₂⋊₂₇D₆	3^rd semidirect product of D₁₂ and D₆ acting through Inn(D₁₂)	24	4+	D12:27D6	288,956
S₃²×D₄	Direct product of S₃, S₃ and D₄	24	8+	S3^2xD4	288,958
Dic₆⋊₁₂D₆	6^th semidirect product of Dic₆ and D₆ acting via D₆/S₃=C₂	24	8+	Dic6:12D6	288,960
D₁₂⋊₁₃D₆	7^th semidirect product of D₁₂ and D₆ acting via D₆/S₃=C₂	24	8+	D12:13D6	288,962
C₂×Dic₃⋊D₆	Direct product of C₂ and Dic₃⋊D₆	24		C2xDic3:D6	288,977
C₃²⋊2₊¹⁺⁴	The semidirect product of C₃² and 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂³=C₂²	24	4	C3^2:ES+(2,2)	288,978
C₃×C₂³⋊A₄	Direct product of C₃ and C₂³⋊A₄	24	4	C3xC2^3:A4	288,987
C₃×D₄⋊₆D₆	Direct product of C₃ and D₄⋊₆D₆	24	4	C3xD4:6D6	288,994
C₂²×S₃≀C₂	Direct product of C₂² and S₃≀C₂	24		C2^2xS3wrC2	288,1031
C₃×C₂²⋊S₄	Direct product of C₃ and C₂²⋊S₄	24	6	C3xC2^2:S4	288,1035
(C₂×C₆)⋊S₄	2^nd semidirect product of C₂×C₆ and S₄ acting via S₄/C₂²=S₃	24	6	(C2xC6):S4	288,1036

Groups of order 336

		d	ρ	Label	ID
S₃×F₈	Direct product of S₃ and F₈	24	14+	S3xF8	336,211

Groups of order 432

		d	ρ	Label	ID
D₆⋊(C₃²⋊C₄)	The semidirect product of D₆ and C₃²⋊C₄ acting via C₃²⋊C₄/C₃⋊S₃=C₂	24	8+	D6:(C3^2:C4)	432,568
C₃³⋊₅(C₂×C₈)	2^nd semidirect product of C₃³ and C₂×C₈ acting via C₂×C₈/C₂=C₂×C₄	24	8+	C3^3:5(C2xC8)	432,571
C₃³⋊₂M₄(2)	2^nd semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₂=C₂×C₄	24	8+	C3^3:2M4(2)	432,573
C₃×S₃²⋊C₄	Direct product of C₃ and S₃²⋊C₄	24	4	C3xS3^2:C4	432,574
C₃×C₃²⋊D₈	Direct product of C₃ and C₃²⋊D₈	24	4	C3xC3^2:D8	432,576
C₃×C₃²⋊₂SD₁₆	Direct product of C₃ and C₃²⋊₂SD₁₆	24	4	C3xC3^2:2SD16	432,577
C₃⋊S₃.₂D₁₂	1^st non-split extension by C₃⋊S₃ of D₁₂ acting via D₁₂/C₆=C₂²	24	4	C3:S3.2D12	432,579
S₃²⋊Dic₃	The semidirect product of S₃² and Dic₃ acting via Dic₃/C₆=C₂	24	4	S3^2:Dic3	432,580
C₃³⋊D₈	2^nd semidirect product of C₃³ and D₈ acting via D₈/C₂=D₄	24	4	C3^3:D8	432,582
C₃³⋊₆SD₁₆	2^nd semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₂=D₄	24	4	C3^3:6SD16	432,583
C₃³⋊₇SD₁₆	3^rd semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₂=D₄	24	4	C3^3:7SD16	432,584
(C₃×C₆).₈D₁₂	1^st non-split extension by C₃×C₆ of D₁₂ acting via D₁₂/C₃=D₄	24	8+	(C3xC6).8D12	432,586
C₃²⋊₂D₂₄	The semidirect product of C₃² and D₂₄ acting via D₂₄/C₆=D₄	24	8+	C3^2:2D24	432,588
C₃³⋊₈SD₁₆	4^th semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₂=D₄	24	8+	C3^3:8SD16	432,589
S₃×C₆.D₆	Direct product of S₃ and C₆.D₆	24	8+	S3xC6.D6	432,595
S₃×C₃⋊D₁₂	Direct product of S₃ and C₃⋊D₁₂	24	8+	S3xC3:D12	432,598
D₆⋊₄S₃²	1^st semidirect product of D₆ and S₃² acting via S₃²/C₃⋊S₃=C₂	24	8+	D6:4S3^2	432,599
(S₃×C₆)⋊D₆	1^st semidirect product of S₃×C₆ and D₆ acting via D₆/C₃=C₂²	24	8+	(S3xC6):D6	432,601
C₃⋊S₃⋊₄D₁₂	The semidirect product of C₃⋊S₃ and D₁₂ acting via D₁₂/D₆=C₂	24	8+	C3:S3:4D12	432,602
C₃³⋊₆(C₂×Q₈)	3^rd semidirect product of C₃³ and C₂×Q₈ acting via C₂×Q₈/C₂=C₂³	24	8+	C3^3:6(C2xQ8)	432,605
(S₃×C₆).D₆	9^th non-split extension by S₃×C₆ of D₆ acting via D₆/C₃=C₂²	24	8+	(S3xC6).D6	432,606
D₆.₃S₃²	3^rd non-split extension by D₆ of S₃² acting via S₃²/C₃×S₃=C₂	24	8+	D6.3S3^2	432,609
Dic₃.S₃²	4^th non-split extension by Dic₃ of S₃² acting via S₃²/C₃×S₃=C₂	24	8+	Dic3.S3^2	432,612
C₃×C₆².C₄	Direct product of C₃ and C₆².C₄	24	4	C3xC6^2.C4	432,633
C₃×C₆²⋊C₄	Direct product of C₃ and C₆²⋊C₄	24	4	C3xC6^2:C4	432,634
C₃³⋊₁₂M₄(2)	2^nd semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₂²=C₄	24	4	C3^3:12M4(2)	432,640
C₆²⋊₁₁Dic₃	1^st semidirect product of C₆² and Dic₃ acting via Dic₃/C₃=C₄	24	4	C6^2:11Dic3	432,641
C₃×D₆.₃D₆	Direct product of C₃ and D₆.₃D₆	24	4	C3xD6.3D6	432,652
C₃×D₆.₄D₆	Direct product of C₃ and D₆.₄D₆	24	4	C3xD6.4D6	432,653
C₃×S₃×C₃⋊D₄	Direct product of C₃, S₃ and C₃⋊D₄	24	4	C3xS3xC3:D4	432,658
C₃×Dic₃⋊D₆	Direct product of C₃ and Dic₃⋊D₆	24	4	C3xDic3:D6	432,659
C₆².₉₆D₆	44^th non-split extension by C₆² of D₆ acting via D₆/C₃=C₂²	24	4	C6^2.96D6	432,693
C₆²⋊₂₄D₆	5^th semidirect product of C₆² and D₆ acting via D₆/C₃=C₂²	24	4	C6^2:24D6	432,696
S₃×F₉	Direct product of S₃ and F₉	24	16+	S3xF9	432,736
C₃×AΓL₁(𝔽₉)	Direct product of C₃ and AΓL₁(𝔽₉)	24	8	C3xAGammaL(1,9)	432,737
C₃³⋊SD₁₆	2^nd semidirect product of C₃³ and SD₁₆ acting faithfully	24	8	C3^3:SD16	432,738
C₃³⋊₃SD₁₆	3^rd semidirect product of C₃³ and SD₁₆ acting faithfully	24	16+	C3^3:3SD16	432,739
F₉⋊S₃	The semidirect product of F₉ and S₃ acting via S₃/C₃=C₂	24	16+	F9:S3	432,740
S₃×PSU₃(𝔽₂)	Direct product of S₃ and PSU₃(𝔽₂)	24	16+	S3xPSU(3,2)	432,742
C₆²⋊Dic₃	The semidirect product of C₆² and Dic₃ acting faithfully	24	12+	C6^2:Dic3	432,743
A₄×C₃²⋊C₄	Direct product of A₄ and C₃²⋊C₄	24	12+	A4xC3^2:C4	432,744
C₃×S₃×S₄	Direct product of C₃, S₃ and S₄	24	6	C3xS3xS4	432,745
S₃×C₃⋊S₄	Direct product of S₃ and C₃⋊S₄	24	12+	S3xC3:S4	432,747
C₆²⋊₁₀D₆	10^th semidirect product of C₆² and D₆ acting faithfully	24	12+	C6^2:10D6	432,748
S₃²×A₄	Direct product of S₃, S₃ and A₄	24	12+	S3^2xA4	432,749
C₂×S₃×C₃²⋊C₄	Direct product of C₂, S₃ and C₃²⋊C₄	24	8+	C2xS3xC3^2:C4	432,753
C₆×S₃≀C₂	Direct product of C₆ and S₃≀C₂	24	4	C6xS3wrC2	432,754
C₂×C₃³⋊D₄	Direct product of C₂ and C₃³⋊D₄	24	4	C2xC3^3:D4	432,755
C₂×C₃²⋊₂D₁₂	Direct product of C₂ and C₃²⋊₂D₁₂	24	8+	C2xC3^2:2D12	432,756
C₂×S₃³	Direct product of C₂, S₃, S₃ and S₃	24	8+	C2xS3^3	432,759

Groups of order 480

		d	ρ	Label	ID
GL₂(𝔽₅)	General linear group on 𝔽₅²; = SL₂(𝔽₅)⋊₁ C₄ = Aut(C₅²)	24	4	GL(2,5)	480,218
A₅⋊Q₈	The semidirect product of A₅ and Q₈ acting via Q₈/C₄=C₂	24	6	A5:Q8	480,945
C₂×A₅⋊C₄	Direct product of C₂ and A₅⋊C₄	24		C2xA5:C4	480,952

On 25 points

Groups of order 25

		d	ρ	Label	ID
C₂₅	Cyclic group	25	1	C25	25,1
C₅²	Elementary abelian group of type [5,5]	25		C5^2	25,2

Groups of order 50

		d	ρ	Label	ID
D₂₅	Dihedral group	25	2+	D25	50,1
C₅⋊D₅	The semidirect product of C₅ and D₅ acting via D₅/C₅=C₂	25		C5:D5	50,4

Groups of order 100

		d	ρ	Label	ID
C₂₅⋊C₄	The semidirect product of C₂₅ and C₄ acting faithfully	25	4+	C25:C4	100,3
C₅⋊F₅	1^st semidirect product of C₅ and F₅ acting via F₅/C₅=C₄	25		C5:F5	100,11

Groups of order 125

		d	ρ	Label	ID
He₅	Heisenberg group; = C₅² ⋊C₅ = 5₊¹⁺²	25	5	He5	125,3
5_-¹⁺²	Extraspecial group	25	5	ES-(5,1)	125,4

Groups of order 250

		d	ρ	Label	ID
C₅²⋊C₁₀	The semidirect product of C₅² and C₁₀ acting faithfully	25	10+	C5^2:C10	250,5
C₂₅⋊C₁₀	The semidirect product of C₂₅ and C₁₀ acting faithfully	25	10+	C25:C10	250,6
He₅⋊C₂	2^nd semidirect product of He₅ and C₂ acting faithfully	25	5	He5:C2	250,8

Groups of order 300

		d	ρ	Label	ID
C₅×A₅	Direct product of C₅ and A₅; = U₂(𝔽₄)	25	3	C5xA5	300,22

Groups of order 500

		d	ρ	Label	ID
C₅²⋊C₂₀	The semidirect product of C₅² and C₂₀ acting faithfully	25	20+	C5^2:C20	500,17
C₂₅⋊C₂₀	The semidirect product of C₂₅ and C₂₀ acting faithfully; = Aut(D₂₅) = Hol(C₂₅)	25	20+	C25:C20	500,18
He₅⋊C₄	2^nd semidirect product of He₅ and C₄ acting faithfully	25	20+	He5:C4	500,21
C₅²⋊F₅	3^rd semidirect product of C₅² and F₅ acting faithfully	25	10+	C5^2:F5	500,23
He₅⋊₄C₄	4^th semidirect product of He₅ and C₄ acting faithfully; = Aut(5_-¹⁺²)	25	5	He5:4C4	500,25
C₅²⋊D₁₀	The semidirect product of C₅² and D₁₀ acting faithfully	25	10+	C5^2:D10	500,27

On 26 points

Groups of order 26

		d	ρ	Label	ID
C₂₆	Cyclic group	26	1	C26	26,2

Groups of order 52

		d	ρ	Label	ID
D₂₆	Dihedral group; = C₂×D₁₃	26	2+	D26	52,4

Groups of order 78

		d	ρ	Label	ID
C₂×C₁₃⋊C₃	Direct product of C₂ and C₁₃⋊C₃	26	3	C2xC13:C3	78,2

Groups of order 104

		d	ρ	Label	ID
C₂×C₁₃⋊C₄	Direct product of C₂ and C₁₃⋊C₄	26	4+	C2xC13:C4	104,12

Groups of order 156

		d	ρ	Label	ID
C₂×C₁₃⋊C₆	Direct product of C₂ and C₁₃⋊C₆	26	6+	C2xC13:C6	156,8

Groups of order 312

		d	ρ	Label	ID
C₂×F₁₃	Direct product of C₂ and F₁₃; = Aut(D₂₆) = Hol(C₂₆)	26	12+	C2xF13	312,45

Groups of order 338

		d	ρ	Label	ID
C₁₃×D₁₃	Direct product of C₁₃ and D₁₃; = AΣL₁(𝔽₁₆₉)	26	2	C13xD13	338,3

On 27 points

Groups of order 27

		d	ρ	Label	ID
C₂₇	Cyclic group	27	1	C27	27,1
C₃×C₉	Abelian group of type [3,9]	27		C3xC9	27,2
C₃³	Elementary abelian group of type [3,3,3]	27		C3^3	27,5

Groups of order 54

		d	ρ	Label	ID
D₂₇	Dihedral group	27	2+	D27	54,1
C₉⋊S₃	The semidirect product of C₉ and S₃ acting via S₃/C₃=C₂	27		C9:S3	54,7
C₃³⋊C₂	3^rd semidirect product of C₃³ and C₂ acting faithfully	27		C3^3:C2	54,14

Groups of order 81

		d	ρ	Label	ID
C₃²⋊C₉	The semidirect product of C₃² and C₉ acting via C₉/C₃=C₃	27		C3^2:C9	81,3
C₂₇⋊C₃	The semidirect product of C₂₇ and C₃ acting faithfully	27	3	C27:C3	81,6
He₃.C₃	The non-split extension by He₃ of C₃ acting faithfully	27	3	He3.C3	81,8
He₃⋊C₃	2^nd semidirect product of He₃ and C₃ acting faithfully	27	3	He3:C3	81,9
C₃.He₃	4^th central stem extension by C₃ of He₃	27	3	C3.He3	81,10
C₃×He₃	Direct product of C₃ and He₃	27		C3xHe3	81,12
C₃×3_-¹⁺²	Direct product of C₃ and 3_-¹⁺²	27		C3xES-(3,1)	81,13
C₉○He₃	Central product of C₉ and He₃	27	3	C9oHe3	81,14

Groups of order 162

		d	ρ	Label	ID
C₃²⋊D₉	1^st semidirect product of C₃² and D₉ acting via D₉/C₃=S₃	27		C3^2:D9	162,5
C₂₇⋊C₆	The semidirect product of C₂₇ and C₆ acting faithfully	27	6+	C27:C6	162,9
He₃.C₆	1^st non-split extension by He₃ of C₆ acting faithfully	27	3	He3.C6	162,12
He₃.S₃	1^st non-split extension by He₃ of S₃ acting faithfully	27	6+	He3.S3	162,13
He₃.₂C₆	2^nd non-split extension by He₃ of C₆ acting faithfully	27	3	He3.2C6	162,14
He₃.₂S₃	2^nd non-split extension by He₃ of S₃ acting faithfully	27	6+	He3.2S3	162,15
He₃.₃S₃	3^rd non-split extension by He₃ of S₃ acting faithfully	27	6+	He3.3S3	162,20
He₃⋊S₃	3^rd semidirect product of He₃ and S₃ acting faithfully	27	6+	He3:S3	162,21
3_-¹⁺².S₃	The non-split extension by 3_-¹⁺² of S₃ acting faithfully	27	6+	ES-(3,1).S3	162,22
He₃⋊₄S₃	1^st semidirect product of He₃ and S₃ acting via S₃/C₃=C₂	27		He3:4S3	162,40
C₃×He₃⋊C₂	Direct product of C₃ and He₃⋊C₂	27		C3xHe3:C2	162,41
C₃³.S₃	4^th non-split extension by C₃³ of S₃ acting faithfully	27		C3^3.S3	162,42
He₃.₄S₃	The non-split extension by He₃ of S₃ acting via S₃/C₃=C₂	27	6+	He3.4S3	162,43
He₃.₄C₆	The non-split extension by He₃ of C₆ acting via C₆/C₃=C₂	27	3	He3.4C6	162,44

Groups of order 216

		d	ρ	Label	ID
He₃⋊C₈	The semidirect product of He₃ and C₈ acting faithfully	27	6+	He3:C8	216,86
SU₃(𝔽₂)	Special unitary group on 𝔽₂³; = He₃ ⋊Q₈	27	3	SU(3,2)	216,88

Groups of order 243

		d	ρ	Label	ID
C₃³⋊C₉	1^st semidirect product of C₃³ and C₉ acting via C₉/C₃=C₃	27		C3^3:C9	243,13
C₉.₄He₃	2^nd central extension by C₉ of He₃	27	3	C9.4He3	243,16
C₂₇⋊C₉	The semidirect product of C₂₇ and C₉ acting faithfully	27	9	C27:C9	243,22
C₉²⋊C₃	1^st semidirect product of C₉² and C₃ acting faithfully	27	3	C9^2:C3	243,25
C₉²⋊₂C₃	2^nd semidirect product of C₉² and C₃ acting faithfully	27	3	C9^2:2C3	243,26
C₉².C₃	2^nd non-split extension by C₉² of C₃ acting faithfully	27	3	C9^2.C3	243,27
C₃².He₃	4^th non-split extension by C₃² of He₃ acting via He₃/C₃²=C₃	27	9	C3^2.He3	243,28
C₃².₅He₃	5^th non-split extension by C₃² of He₃ acting via He₃/C₃²=C₃	27	9	C3^2.5He3	243,29
C₃².₆He₃	6^th non-split extension by C₃² of He₃ acting via He₃/C₃²=C₃	27	9	C3^2.6He3	243,30
C₃²⋊He₃	The semidirect product of C₃² and He₃ acting via He₃/C₃²=C₃	27		C3^2:He3	243,37
C₃⁴.C₃	3^rd non-split extension by C₃⁴ of C₃ acting faithfully	27		C3^4.C3	243,38
C₃×C₃≀C₃	Direct product of C₃ and C₃≀C₃	27		C3xC3wrC3	243,51
C₉.He₃	1^st non-split extension by C₉ of He₃ acting via He₃/C₃²=C₃	27	3	C9.He3	243,55
C₃³⋊C₃²	2^nd semidirect product of C₃³ and C₃² acting faithfully	27	9	C3^3:C3^2	243,56
He₃.C₃²	4^th non-split extension by He₃ of C₃² acting via C₃²/C₃=C₃	27	9	He3.C3^2	243,57
He₃⋊C₃²	3^rd semidirect product of He₃ and C₃² acting via C₃²/C₃=C₃	27	9	He3:C3^2	243,58
C₃².C₃³	9^th non-split extension by C₃² of C₃³ acting via C₃³/C₃²=C₃	27	9	C3^2.C3^3	243,59
C₉.₂He₃	2^nd non-split extension by C₉ of He₃ acting via He₃/C₃²=C₃	27	9	C9.2He3	243,60
3₊¹⁺⁴	Extraspecial group; = He₃ ○He₃	27	9	ES+(3,2)	243,65
3_-¹⁺⁴	Extraspecial group; = He₃ ○3_-¹⁺²	27	9	ES-(3,2)	243,66

Groups of order 324

		d	ρ	Label	ID
He₃.D₆	1^st non-split extension by He₃ of D₆ acting faithfully	27	6+	He3.D6	324,40
He₃.₂D₆	2^nd non-split extension by He₃ of D₆ acting faithfully	27	6+	He3.2D6	324,41
He₃⋊₆D₆	2^nd semidirect product of He₃ and D₆ acting via D₆/C₃=C₂²	27		He3:6D6	324,124
He₃.₆D₆	The non-split extension by He₃ of D₆ acting via D₆/C₃=C₂²	27	6+	He3.6D6	324,125

Groups of order 351

		d	ρ	Label	ID
C₃³⋊C₁₃	The semidirect product of C₃³ and C₁₃ acting faithfully	27	13	C3^3:C13	351,12

Groups of order 432

		d	ρ	Label	ID
He₃⋊SD₁₆	The semidirect product of He₃ and SD₁₆ acting faithfully	27	6+	He3:SD16	432,520

Groups of order 486

		d	ρ	Label	ID
C₂₇⋊C₁₈	The semidirect product of C₂₇ and C₁₈ acting faithfully; = Aut(D₂₇) = Hol(C₂₇)	27	18+	C27:C18	486,31
C₉²⋊C₆	1^st semidirect product of C₉² and C₆ acting faithfully	27	6+	C9^2:C6	486,35
C₉²⋊S₃	1^st semidirect product of C₉² and S₃ acting faithfully	27	6+	C9^2:S3	486,36
C₉²⋊₂C₆	2^nd semidirect product of C₉² and C₆ acting faithfully	27	6+	C9^2:2C6	486,37
C₉².S₃	2^nd non-split extension by C₉² of S₃ acting faithfully	27	6+	C9^2.S3	486,38
C₉⋊C₉.S₃	2^nd non-split extension by C₉⋊C₉ of S₃ acting faithfully	27	18+	C9:C9.S3	486,39
C₉⋊C₉.₃S₃	3^rd non-split extension by C₉⋊C₉ of S₃ acting faithfully	27	18+	C9:C9.3S3	486,40
C₉⋊C₉⋊S₃	1^st semidirect product of C₉⋊C₉ and S₃ acting faithfully	27	18+	C9:C9:S3	486,41
C₃³⋊₂D₉	2^nd semidirect product of C₃³ and D₉ acting via D₉/C₃=S₃	27		C3^3:2D9	486,52
C₃³.D₉	3^rd non-split extension by C₃³ of D₉ acting via D₉/C₃=S₃	27	6+	C3^3.D9	486,55
C₉²⋊₂S₃	2^nd semidirect product of C₉² and S₃ acting faithfully	27	3	C9^2:2S3	486,61
C₃⁴⋊S₃	1^st semidirect product of C₃⁴ and S₃ acting faithfully	27		C3^4:S3	486,103
C₃⁴.S₃	4^th non-split extension by C₃⁴ of S₃ acting faithfully	27		C3^4.S3	486,105
C₃×C₃≀S₃	Direct product of C₃ and C₃≀S₃	27		C3xC3wrS3	486,115
C₃≀S₃⋊₃C₃	The semidirect product of C₃≀S₃ and C₃ acting through Inn(C₃≀S₃)	27	3	C3wrS3:3C3	486,125
C₃≀C₃⋊C₆	2^nd semidirect product of C₃≀C₃ and C₆ acting faithfully	27	9	C3wrC3:C6	486,126
(C₃×He₃)⋊C₆	8^th semidirect product of C₃×He₃ and C₆ acting faithfully	27	18+	(C3xHe3):C6	486,127
He₃.C₃⋊C₆	3^rd semidirect product of He₃.C₃ and C₆ acting faithfully	27	9	He3.C3:C6	486,128
C₉⋊S₃⋊C₃²	2^nd semidirect product of C₉⋊S₃ and C₃² acting faithfully	27	18+	C9:S3:C3^2	486,129
He₃.(C₃×C₆)	6^th non-split extension by He₃ of C₃×C₆ acting via C₃×C₆/C₃=C₆	27	9	He3.(C3xC6)	486,130
He₃.(C₃×S₃)	5^th non-split extension by He₃ of C₃×S₃ acting via C₃×S₃/C₃=S₃	27	18+	He3.(C3xS3)	486,131
C₃≀C₃.C₆	The non-split extension by C₃≀C₃ of C₆ acting faithfully	27	9	C3wrC3.C6	486,132
C₃⁴⋊₄C₆	4^th semidirect product of C₃⁴ and C₆ acting faithfully	27		C3^4:4C6	486,146
C₃⁴⋊₅C₆	5^th semidirect product of C₃⁴ and C₆ acting faithfully	27		C3^4:5C6	486,167
C₃≀C₃.S₃	The non-split extension by C₃≀C₃ of S₃ acting via S₃/C₃=C₂	27	6+	C3wrC3.S3	486,175
C₃³⋊(C₃×S₃)	4^th semidirect product of C₃³ and C₃×S₃ acting faithfully	27	18+	C3^3:(C3xS3)	486,176
He₃.C₃⋊₂C₆	2^nd semidirect product of He₃.C₃ and C₆ acting faithfully	27	18+	He3.C3:2C6	486,177
He₃⋊(C₃×S₃)	4^th semidirect product of He₃ and C₃×S₃ acting via C₃×S₃/C₃=S₃	27	18+	He3:(C3xS3)	486,178
C₃.He₃⋊C₆	The semidirect product of C₃.He₃ and C₆ acting faithfully	27	18+	C3.He3:C6	486,179
C₃⁴⋊₆S₃	6^th semidirect product of C₃⁴ and S₃ acting faithfully	27		C3^4:6S3	486,183
C₃⁴⋊₇S₃	7^th semidirect product of C₃⁴ and S₃ acting faithfully	27		C3^4:7S3	486,185
C₃≀C₃⋊S₃	2^nd semidirect product of C₃≀C₃ and S₃ acting via S₃/C₃=C₂	27	6+	C3wrC3:S3	486,189
3₊¹⁺⁴⋊C₂	1^st semidirect product of 3₊¹⁺⁴ and C₂ acting faithfully	27	18+	ES+(3,2):C2	486,236
3₊¹⁺⁴⋊₂C₂	2^nd semidirect product of 3₊¹⁺⁴ and C₂ acting faithfully	27	9	ES+(3,2):2C2	486,237
3_-¹⁺⁴⋊C₂	1^st semidirect product of 3_-¹⁺⁴ and C₂ acting faithfully	27	18+	ES-(3,2):C2	486,238
3_-¹⁺⁴⋊₂C₂	2^nd semidirect product of 3_-¹⁺⁴ and C₂ acting faithfully	27	9	ES-(3,2):2C2	486,239
3₊¹⁺⁴⋊₃C₂	3^rd semidirect product of 3₊¹⁺⁴ and C₂ acting faithfully	27	9	ES+(3,2):3C2	486,249

On 28 points

Groups of order 28

		d	ρ	Label	ID
Dic₇	Dicyclic group; = C₇ ⋊C₄	28	2-	Dic7	28,1
C₂₈	Cyclic group	28	1	C28	28,2
C₂×C₁₄	Abelian group of type [2,14]	28		C2xC14	28,4

Groups of order 56

		d	ρ	Label	ID
C₄×D₇	Direct product of C₄ and D₇	28	2	C4xD7	56,4
D₂₈	Dihedral group	28	2+	D28	56,5
C₇⋊D₄	The semidirect product of C₇ and D₄ acting via D₄/C₂²=C₂	28	2	C7:D4	56,7
C₇×D₄	Direct product of C₇ and D₄	28	2	C7xD4	56,9
C₂²×D₇	Direct product of C₂² and D₇	28		C2^2xD7	56,12

Groups of order 84

		d	ρ	Label	ID
C₇⋊C₁₂	The semidirect product of C₇ and C₁₂ acting via C₁₂/C₂=C₆	28	6-	C7:C12	84,1
C₄×C₇⋊C₃	Direct product of C₄ and C₇⋊C₃	28	3	C4xC7:C3	84,2
C₂²×C₇⋊C₃	Direct product of C₂² and C₇⋊C₃	28		C2^2xC7:C3	84,9
C₇×A₄	Direct product of C₇ and A₄	28	3	C7xA4	84,10
C₇⋊A₄	The semidirect product of C₇ and A₄ acting via A₄/C₂²=C₃	28	3	C7:A4	84,11

Groups of order 112

		d	ρ	Label	ID
D₄×D₇	Direct product of D₄ and D₇	28	4+	D4xD7	112,31

Groups of order 168

		d	ρ	Label	ID
C₄×F₇	Direct product of C₄ and F₇	28	6	C4xF7	168,8
C₄⋊F₇	The semidirect product of C₄ and F₇ acting via F₇/C₇⋊C₃=C₂	28	6+	C4:F7	168,9
Dic₇⋊C₆	The semidirect product of Dic₇ and C₆ acting faithfully	28	6	Dic7:C6	168,11
D₄×C₇⋊C₃	Direct product of D₄ and C₇⋊C₃	28	6	D4xC7:C3	168,20
C₇×S₄	Direct product of C₇ and S₄	28	3	C7xS4	168,45
C₇⋊S₄	The semidirect product of C₇ and S₄ acting via S₄/A₄=C₂	28	6+	C7:S4	168,46
C₂²×F₇	Direct product of C₂² and F₇	28		C2^2xF7	168,47
A₄×D₇	Direct product of A₄ and D₇	28	6+	A4xD7	168,48
D₇⋊A₄	The semidirect product of D₇ and A₄ acting via A₄/C₂²=C₃	28	6+	D7:A4	168,49

Groups of order 196

		d	ρ	Label	ID
C₇×Dic₇	Direct product of C₇ and Dic₇	28	2	C7xDic7	196,5
D₇×C₁₄	Direct product of C₁₄ and D₇	28	2	D7xC14	196,10

Groups of order 224

		d	ρ	Label	ID
C₄×F₈	Direct product of C₄ and F₈	28	7	C4xF8	224,173
C₂²×F₈	Direct product of C₂² and F₈	28		C2^2xF8	224,195

Groups of order 252

		d	ρ	Label	ID
A₄×C₇⋊C₃	Direct product of A₄ and C₇⋊C₃	28	9	A4xC7:C3	252,27

Groups of order 336

		d	ρ	Label	ID
D₄×F₇	Direct product of D₄ and F₇; = Aut(D₂₈) = Hol(C₂₈)	28	12+	D4xF7	336,125
D₇×S₄	Direct product of D₇ and S₄	28	6+	D7xS4	336,212

Groups of order 392

		d	ρ	Label	ID
Dic₇⋊₂D₇	The semidirect product of Dic₇ and D₇ acting through Inn(Dic₇)	28	4+	Dic7:2D7	392,19
C₇⋊D₂₈	The semidirect product of C₇ and D₂₈ acting via D₂₈/D₁₄=C₂	28	4+	C7:D28	392,21
C₇×C₇⋊D₄	Direct product of C₇ and C₇⋊D₄	28	2	C7xC7:D4	392,27
C₇²⋊C₈	The semidirect product of C₇² and C₈ acting faithfully	28	8+	C7^2:C8	392,36
C₇²⋊Q₈	The semidirect product of C₇² and Q₈ acting faithfully	28	8+	C7^2:Q8	392,38
C₂×C₇²⋊C₄	Direct product of C₂ and C₇²⋊C₄	28	4+	C2xC7^2:C4	392,40
C₂×D₇²	Direct product of C₂, D₇ and D₇	28	4+	C2xD7^2	392,41

Groups of order 448

		d	ρ	Label	ID
C₄³⋊C₇	The semidirect product of C₄³ and C₇ acting faithfully	28	7	C4^3:C7	448,178
D₄×F₈	Direct product of D₄ and F₈	28	14+	D4xF8	448,1363
C₂⁶⋊C₇	2^nd semidirect product of C₂⁶ and C₇ acting faithfully	28		C2^6:C7	448,1393

On 29 points

Groups of order 29

		d	ρ	Label	ID
C₂₉	Cyclic group	29	1	C29	29,1

Groups of order 58

		d	ρ	Label	ID
D₂₉	Dihedral group	29	2+	D29	58,1

Groups of order 116

		d	ρ	Label	ID
C₂₉⋊C₄	The semidirect product of C₂₉ and C₄ acting faithfully	29	4+	C29:C4	116,3

Groups of order 203

		d	ρ	Label	ID
C₂₉⋊C₇	The semidirect product of C₂₉ and C₇ acting faithfully	29	7	C29:C7	203,1

Groups of order 406

		d	ρ	Label	ID
C₂₉⋊C₁₄	The semidirect product of C₂₉ and C₁₄ acting faithfully	29	14+	C29:C14	406,1

On 30 points

Groups of order 30

		d	ρ	Label	ID
C₃₀	Cyclic group	30	1	C30	30,4

Groups of order 60

		d	ρ	Label	ID
C₆×D₅	Direct product of C₆ and D₅	30	2	C6xD5	60,10
S₃×C₁₀	Direct product of C₁₀ and S₃	30	2	S3xC10	60,11
D₃₀	Dihedral group; = C₂×D₁₅	30	2+	D30	60,12

Groups of order 90

		d	ρ	Label	ID
S₃×C₁₅	Direct product of C₁₅ and S₃	30	2	S3xC15	90,6
C₃×D₁₅	Direct product of C₃ and D₁₅	30	2	C3xD15	90,7

Groups of order 120

		d	ρ	Label	ID
C₆×F₅	Direct product of C₆ and F₅	30	4	C6xF5	120,40
C₂×C₃⋊F₅	Direct product of C₂ and C₃⋊F₅	30	4	C2xC3:F5	120,41
C₂×S₃×D₅	Direct product of C₂, S₃ and D₅	30	4+	C2xS3xD5	120,42
C₁₀×A₄	Direct product of C₁₀ and A₄	30	3	C10xA4	120,43

Groups of order 150

		d	ρ	Label	ID
C₂×C₅²⋊C₃	Direct product of C₂ and C₅²⋊C₃	30	3	C2xC5^2:C3	150,7
D₅×C₁₅	Direct product of C₁₅ and D₅	30	2	D5xC15	150,8
C₅×D₁₅	Direct product of C₅ and D₁₅	30	2	C5xD15	150,11

Groups of order 180

		d	ρ	Label	ID
C₃×C₃⋊F₅	Direct product of C₃ and C₃⋊F₅	30	4	C3xC3:F5	180,21
C₅×C₃²⋊C₄	Direct product of C₅ and C₃²⋊C₄	30	4	C5xC3^2:C4	180,23
C₃²⋊Dic₅	The semidirect product of C₃² and Dic₅ acting via Dic₅/C₅=C₄	30	4	C3^2:Dic5	180,24
C₃²⋊F₅	The semidirect product of C₃² and F₅ acting via F₅/C₅=C₄	30	4+	C3^2:F5	180,25
C₃×S₃×D₅	Direct product of C₃, S₃ and D₅	30	4	C3xS3xD5	180,26
C₅×S₃²	Direct product of C₅, S₃ and S₃	30	4	C5xS3^2	180,28
S₃×D₁₅	Direct product of S₃ and D₁₅	30	4+	S3xD15	180,29
D₁₅⋊S₃	The semidirect product of D₁₅ and S₃ acting via S₃/C₃=C₂	30	4	D15:S3	180,30

Groups of order 240

		d	ρ	Label	ID
C₂×S₃×F₅	Direct product of C₂, S₃ and F₅; = Aut(D₃₀) = Hol(C₃₀)	30	8+	C2xS3xF5	240,195
C₁₀×S₄	Direct product of C₁₀ and S₄	30	3	C10xS4	240,196
C₂×C₅⋊S₄	Direct product of C₂ and C₅⋊S₄	30	6+	C2xC5:S4	240,197
C₂×D₅×A₄	Direct product of C₂, D₅ and A₄	30	6+	C2xD5xA4	240,198
C₃×C₂⁴⋊C₅	Direct product of C₃ and C₂⁴⋊C₅	30	5	C3xC2^4:C5	240,199

Groups of order 300

		d	ρ	Label	ID
C₂×C₅²⋊S₃	Direct product of C₂ and C₅²⋊S₃	30	3	C2xC5^2:S3	300,26
C₂×C₅²⋊C₆	Direct product of C₂ and C₅²⋊C₆	30	6+	C2xC5^2:C6	300,27
C₃×C₅²⋊C₄	Direct product of C₃ and C₅²⋊C₄	30	4	C3xC5^2:C4	300,31
C₁₅⋊₂F₅	2^nd semidirect product of C₁₅ and F₅ acting via F₅/C₅=C₄	30	4	C15:2F5	300,35
C₃×D₅²	Direct product of C₃, D₅ and D₅	30	4	C3xD5^2	300,36
C₅×S₃×D₅	Direct product of C₅, S₃ and D₅	30	4	C5xS3xD5	300,37
D₅×D₁₅	Direct product of D₅ and D₁₅	30	4+	D5xD15	300,39
D₁₅⋊D₅	The semidirect product of D₁₅ and D₅ acting via D₅/C₅=C₂	30	4	D15:D5	300,40
C₅²⋊A₄	The semidirect product of C₅² and A₄ acting via A₄/C₂²=C₃	30	3	C5^2:A4	300,43

Groups of order 360

		d	ρ	Label	ID
C₆×A₅	Direct product of C₆ and A₅	30	3	C6xA5	360,122
C₃×S₃×F₅	Direct product of C₃, S₃ and F₅	30	8	C3xS3xF5	360,126
S₃×C₃⋊F₅	Direct product of S₃ and C₃⋊F₅	30	8	S3xC3:F5	360,128
C₃⋊F₅⋊S₃	The semidirect product of C₃⋊F₅ and S₃ acting via S₃/C₃=C₂	30	8+	C3:F5:S3	360,129
D₅×C₃²⋊C₄	Direct product of D₅ and C₃²⋊C₄	30	8+	D5xC3^2:C4	360,130
C₃²⋊F₅⋊C₂	The semidirect product of C₃²⋊F₅ and C₂ acting faithfully	30	8+	C3^2:F5:C2	360,131
C₅×S₃≀C₂	Direct product of C₅ and S₃≀C₂	30	4	C5xS3wrC2	360,132
S₃²⋊D₅	The semidirect product of S₃² and D₅ acting via D₅/C₅=C₂	30	4	S3^2:D5	360,133
C₃²⋊D₂₀	The semidirect product of C₃² and D₂₀ acting via D₂₀/C₅=D₄	30	8+	C3^2:D20	360,134
S₃²×D₅	Direct product of S₃, S₃ and D₅	30	8+	S3^2xD5	360,137

Groups of order 450

		d	ρ	Label	ID
C₁₅×D₁₅	Direct product of C₁₅ and D₁₅	30	2	C15xD15	450,29

Groups of order 480

		d	ρ	Label	ID
C₂×F₁₆	Direct product of C₂ and F₁₆	30	15+	C2xF16	480,1190
C₂×A₄⋊F₅	Direct product of C₂ and A₄⋊F₅	30	12+	C2xA4:F5	480,1191
C₂×A₄×F₅	Direct product of C₂, A₄ and F₅	30	12+	C2xA4xF5	480,1192
C₂×D₅×S₄	Direct product of C₂, D₅ and S₄	30	6+	C2xD5xS4	480,1193
C₃×C₂⁴⋊D₅	Direct product of C₃ and C₂⁴⋊D₅	30	5	C3xC2^4:D5	480,1194
C₂⁴⋊D₁₅	The semidirect product of C₂⁴ and D₁₅ acting via D₁₅/C₃=D₅	30	10+	C2^4:D15	480,1195
S₃×C₂⁴⋊C₅	Direct product of S₃ and C₂⁴⋊C₅	30	10+	S3xC2^4:C5	480,1196
C₆×C₂⁴⋊C₅	Direct product of C₆ and C₂⁴⋊C₅	30	5	C6xC2^4:C5	480,1204

On 31 points

Groups of order 31

		d	ρ	Label	ID
C₃₁	Cyclic group	31	1	C31	31,1

Groups of order 62

		d	ρ	Label	ID
D₃₁	Dihedral group	31	2+	D31	62,1

Groups of order 93

		d	ρ	Label	ID
C₃₁⋊C₃	The semidirect product of C₃₁ and C₃ acting faithfully	31	3	C31:C3	93,1

Groups of order 155

		d	ρ	Label	ID
C₃₁⋊C₅	The semidirect product of C₃₁ and C₅ acting faithfully	31	5	C31:C5	155,1

Groups of order 186

		d	ρ	Label	ID
C₃₁⋊C₆	The semidirect product of C₃₁ and C₆ acting faithfully	31	6+	C31:C6	186,1

Groups of order 310

		d	ρ	Label	ID
C₃₁⋊C₁₀	The semidirect product of C₃₁ and C₁₀ acting faithfully	31	10+	C31:C10	310,1

Groups of order 465

		d	ρ	Label	ID
C₃₁⋊C₁₅	The semidirect product of C₃₁ and C₁₅ acting faithfully	31	15	C31:C15	465,1

On 32 points

Groups of order 32

		d	ρ	Label	ID
C₃₂	Cyclic group	32	1	C32	32,1
C₂.C₄²	1^st central stem extension by C₂ of C₄²	32		C2.C4^2	32,2
C₄×C₈	Abelian group of type [4,8]	32		C4xC8	32,3
C₈⋊C₄	3^rd semidirect product of C₈ and C₄ acting via C₄/C₂=C₂	32		C8:C4	32,4
Q₈⋊C₄	1^st semidirect product of Q₈ and C₄ acting via C₄/C₂=C₂	32		Q8:C4	32,10
C₄⋊C₈	The semidirect product of C₄ and C₈ acting via C₈/C₄=C₂	32		C4:C8	32,12
C₄.Q₈	1^st non-split extension by C₄ of Q₈ acting via Q₈/C₄=C₂	32		C4.Q8	32,13
C₂.D₈	2^nd central extension by C₂ of D₈	32		C2.D8	32,14
C₂×C₁₆	Abelian group of type [2,16]	32		C2xC16	32,16
Q₃₂	Generalised quaternion group; = C₁₆ .C₂ = Dic₈	32	2-	Q32	32,20
C₂×C₄²	Abelian group of type [2,4,4]	32		C2xC4^2	32,21
C₂×C₄⋊C₄	Direct product of C₂ and C₄⋊C₄	32		C2xC4:C4	32,23
C₄×Q₈	Direct product of C₄ and Q₈	32		C4xQ8	32,26
C₄².C₂	4^th non-split extension by C₄² of C₂ acting faithfully	32		C4^2.C2	32,32
C₄⋊Q₈	The semidirect product of C₄ and Q₈ acting via Q₈/C₄=C₂	32		C4:Q8	32,35
C₂²×C₈	Abelian group of type [2,2,8]	32		C2^2xC8	32,36
C₂×Q₁₆	Direct product of C₂ and Q₁₆	32		C2xQ16	32,41
C₂³×C₄	Abelian group of type [2,2,2,4]	32		C2^3xC4	32,45
C₂²×Q₈	Direct product of C₂² and Q₈	32		C2^2xQ8	32,47
C₂⁵	Elementary abelian group of type [2,2,2,2,2]	32		C2^5	32,51

Groups of order 64

		d	ρ	Label	ID
C₂².M₄(2)	2^nd non-split extension by C₂² of M₄(2) acting via M₄(2)/C₂×C₄=C₂	32		C2^2.M4(2)	64,5
D₄⋊C₈	The semidirect product of D₄ and C₈ acting via C₈/C₄=C₂	32		D4:C8	64,6
C₄².C₂²	1^st non-split extension by C₄² of C₂² acting faithfully	32		C4^2.C2^2	64,10
C₄.D₈	1^st non-split extension by C₄ of D₈ acting via D₈/D₄=C₂	32		C4.D8	64,12
C₄.C₄²	3^rd non-split extension by C₄ of C₄² acting via C₄²/C₂×C₄=C₂	32		C4.C4^2	64,22
C₂².C₄²	2^nd non-split extension by C₂² of C₄² acting via C₄²/C₂×C₄=C₂	32		C2^2.C4^2	64,24
C₂²⋊C₁₆	The semidirect product of C₂² and C₁₆ acting via C₁₆/C₈=C₂	32		C2^2:C16	64,29
D₄.C₈	The non-split extension by D₄ of C₈ acting via C₈/C₄=C₂	32	2	D4.C8	64,31
C₂.D₁₆	1^st central extension by C₂ of D₁₆	32		C2.D16	64,38
D₈.C₄	1^st non-split extension by D₈ of C₄ acting via C₄/C₂=C₂	32	2	D8.C4	64,40
C₈.₁₇D₄	4^th non-split extension by C₈ of D₄ acting via D₄/C₂²=C₂	32	4-	C8.17D4	64,43
C₈.₄Q₈	3^rd non-split extension by C₈ of Q₈ acting via Q₈/C₄=C₂	32	2	C8.4Q8	64,49
M₆(2)	Modular maximal-cyclic group; = C₃₂ ⋊₃ C₂	32	2	M6(2)	64,51
D₃₂	Dihedral group	32	2+	D32	64,52
SD₆₄	Semidihedral group; = C₃₂ ⋊₂ C₂ = QD₆₄	32	2	SD64	64,53
C₄×C₂²⋊C₄	Direct product of C₄ and C₂²⋊C₄	32		C4xC2^2:C4	64,58
C₂³.₇Q₈	2^nd non-split extension by C₂³ of Q₈ acting via Q₈/C₄=C₂	32		C2^3.7Q8	64,61
C₂³.₃₄D₄	5^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	32		C2^3.34D4	64,62
C₂³.₈Q₈	3^rd non-split extension by C₂³ of Q₈ acting via Q₈/C₄=C₂	32		C2^3.8Q8	64,66
C₂³.₂₃D₄	2^nd non-split extension by C₂³ of D₄ acting via D₄/C₄=C₂	32		C2^3.23D4	64,67
C₂⁴.C₂²	2^nd non-split extension by C₂⁴ of C₂² acting faithfully	32		C2^4.C2^2	64,69
C₂⁴.₃C₂²	3^rd non-split extension by C₂⁴ of C₂² acting faithfully	32		C2^4.3C2^2	64,71
C₂³⋊₂D₄	1^st semidirect product of C₂³ and D₄ acting via D₄/C₂=C₂²	32		C2^3:2D4	64,73
C₂³⋊Q₈	1^st semidirect product of C₂³ and Q₈ acting via Q₈/C₂=C₂²	32		C2^3:Q8	64,74
C₂³.₁₀D₄	3^rd non-split extension by C₂³ of D₄ acting via D₄/C₂=C₂²	32		C2^3.10D4	64,75
C₂³.Q₈	3^rd non-split extension by C₂³ of Q₈ acting via Q₈/C₂=C₂²	32		C2^3.Q8	64,77
C₂³.₁₁D₄	4^th non-split extension by C₂³ of D₄ acting via D₄/C₂=C₂²	32		C2^3.11D4	64,78
C₂³.₄Q₈	4^th non-split extension by C₂³ of Q₈ acting via Q₈/C₂=C₂²	32		C2^3.4Q8	64,80
C₄×M₄(2)	Direct product of C₄ and M₄(2)	32		C4xM4(2)	64,85
C₈○₂M₄(2)	Central product of C₈ and M₄(2)	32		C8o2M4(2)	64,86
C₂×C₂²⋊C₈	Direct product of C₂ and C₂²⋊C₈	32		C2xC2^2:C8	64,87
(C₂²×C₈)⋊C₂	2^nd semidirect product of C₂²×C₈ and C₂ acting faithfully	32		(C2^2xC8):C2	64,89
C₂×C₄.₁₀D₄	Direct product of C₂ and C₄.₁₀D₄	32		C2xC4.10D4	64,93
C₂×D₄⋊C₄	Direct product of C₂ and D₄⋊C₄	32		C2xD4:C4	64,95
C₂³.₂₄D₄	3^rd non-split extension by C₂³ of D₄ acting via D₄/C₄=C₂	32		C2^3.24D4	64,97
C₂³.₃₆D₄	7^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	32		C2^3.36D4	64,98
C₂³.₃₈D₄	9^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	32		C2^3.38D4	64,100
C₄⋊M₄(2)	The semidirect product of C₄ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	32		C4:M4(2)	64,104
C₄².₆C₂²	6^th non-split extension by C₄² of C₂² acting faithfully	32		C4^2.6C2^2	64,105
C₂³.₂₅D₄	4^th non-split extension by C₂³ of D₄ acting via D₄/C₄=C₂	32		C2^3.25D4	64,108
M₄(2)⋊C₄	1^st semidirect product of M₄(2) and C₄ acting via C₄/C₂=C₂	32		M4(2):C4	64,109
C₂×C₈.C₄	Direct product of C₂ and C₈.C₄	32		C2xC8.C4	64,110
C₄².₁₂C₄	9^th non-split extension by C₄² of C₄ acting via C₄/C₂=C₂	32		C4^2.12C4	64,112
C₄².₆C₄	3^rd non-split extension by C₄² of C₄ acting via C₄/C₂=C₂	32		C4^2.6C4	64,113
C₄².₇C₂²	7^th non-split extension by C₄² of C₂² acting faithfully	32		C4^2.7C2^2	64,114
C₈×D₄	Direct product of C₈ and D₄	32		C8xD4	64,115
C₈⋊₉D₄	3^rd semidirect product of C₈ and D₄ acting via D₄/C₂²=C₂	32		C8:9D4	64,116
C₈⋊₆D₄	3^rd semidirect product of C₈ and D₄ acting via D₄/C₄=C₂	32		C8:6D4	64,117
C₄×D₈	Direct product of C₄ and D₈	32		C4xD8	64,118
C₄×SD₁₆	Direct product of C₄ and SD₁₆	32		C4xSD16	64,119
SD₁₆⋊C₄	1^st semidirect product of SD₁₆ and C₄ acting via C₄/C₂=C₂	32		SD16:C4	64,121
D₈⋊C₄	3^rd semidirect product of D₈ and C₄ acting via C₄/C₂=C₂; = Aut(SD₃₂)	32		D8:C4	64,123
Q₈⋊D₄	1^st semidirect product of Q₈ and D₄ acting via D₄/C₂²=C₂	32		Q8:D4	64,129
D₄⋊D₄	2^nd semidirect product of D₄ and D₄ acting via D₄/C₂²=C₂	32		D4:D4	64,130
C₂²⋊Q₁₆	The semidirect product of C₂² and Q₁₆ acting via Q₁₆/Q₈=C₂	32		C2^2:Q16	64,132
D₄.₇D₄	2^nd non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	32		D4.7D4	64,133
C₄⋊D₈	The semidirect product of C₄ and D₈ acting via D₈/D₄=C₂	32		C4:D8	64,140
C₄⋊SD₁₆	The semidirect product of C₄ and SD₁₆ acting via SD₁₆/Q₈=C₂	32		C4:SD16	64,141
D₄.D₄	1^st non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	32		D4.D4	64,142
D₄.₂D₄	2^nd non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	32		D4.2D4	64,144
Q₈.D₄	2^nd non-split extension by Q₈ of D₄ acting via D₄/C₄=C₂	32		Q8.D4	64,145
C₈⋊₈D₄	2^nd semidirect product of C₈ and D₄ acting via D₄/C₂²=C₂	32		C8:8D4	64,146
C₈⋊₇D₄	1^st semidirect product of C₈ and D₄ acting via D₄/C₂²=C₂	32		C8:7D4	64,147
C₈.₁₈D₄	5^th non-split extension by C₈ of D₄ acting via D₄/C₂²=C₂	32		C8.18D4	64,148
C₈⋊D₄	1^st semidirect product of C₈ and D₄ acting via D₄/C₂=C₂²	32		C8:D4	64,149
C₈⋊₂D₄	2^nd semidirect product of C₈ and D₄ acting via D₄/C₂=C₂²	32		C8:2D4	64,150
C₈.D₄	1^st non-split extension by C₈ of D₄ acting via D₄/C₂=C₂²	32		C8.D4	64,151
D₄.₅D₄	5^th non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	32	4-	D4.5D4	64,154
D₄⋊Q₈	1^st semidirect product of D₄ and Q₈ acting via Q₈/C₄=C₂	32		D4:Q8	64,155
D₄⋊₂Q₈	2^nd semidirect product of D₄ and Q₈ acting via Q₈/C₄=C₂	32		D4:2Q8	64,157
D₄.Q₈	The non-split extension by D₄ of Q₈ acting via Q₈/C₄=C₂	32		D4.Q8	64,159
C₂².D₈	3^rd non-split extension by C₂² of D₈ acting via D₈/D₄=C₂	32		C2^2.D8	64,161
C₂³.₄₆D₄	17^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	32		C2^3.46D4	64,162
C₂³.₁₉D₄	12^nd non-split extension by C₂³ of D₄ acting via D₄/C₂=C₂²	32		C2^3.19D4	64,163
C₂³.₄₇D₄	18^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	32		C2^3.47D4	64,164
C₂³.₄₈D₄	19^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	32		C2^3.48D4	64,165
C₂³.₂₀D₄	13^rd non-split extension by C₂³ of D₄ acting via D₄/C₂=C₂²	32		C2^3.20D4	64,166
C₄.₄D₈	4^th non-split extension by C₄ of D₈ acting via D₈/C₈=C₂	32		C4.4D8	64,167
C₄².₇₈C₂²	21^st non-split extension by C₄² of C₂² acting via C₂²/C₂=C₂	32		C4^2.78C2^2	64,169
C₄².₂₈C₂²	28^th non-split extension by C₄² of C₂² acting faithfully	32		C4^2.28C2^2	64,170
C₄².₂₉C₂²	29^th non-split extension by C₄² of C₂² acting faithfully	32		C4^2.29C2^2	64,171
C₈⋊₅D₄	2^nd semidirect product of C₈ and D₄ acting via D₄/C₄=C₂	32		C8:5D4	64,173
C₈⋊₄D₄	1^st semidirect product of C₈ and D₄ acting via D₄/C₄=C₂	32		C8:4D4	64,174
C₈.₁₂D₄	8^th non-split extension by C₈ of D₄ acting via D₄/C₄=C₂	32		C8.12D4	64,176
C₈⋊₃D₄	3^rd semidirect product of C₈ and D₄ acting via D₄/C₂=C₂²	32		C8:3D4	64,177
C₈.₂D₄	2^nd non-split extension by C₈ of D₄ acting via D₄/C₂=C₂²	32		C8.2D4	64,178
C₂×M₅(2)	Direct product of C₂ and M₅(2)	32		C2xM5(2)	64,184
D₄○C₁₆	Central product of D₄ and C₁₆	32	2	D4oC16	64,185
C₂×D₁₆	Direct product of C₂ and D₁₆	32		C2xD16	64,186
C₂×SD₃₂	Direct product of C₂ and SD₃₂	32		C2xSD32	64,187
C₄○D₁₆	Central product of C₄ and D₁₆	32	2	C4oD16	64,189
Q₃₂⋊C₂	2^nd semidirect product of Q₃₂ and C₂ acting faithfully	32	4-	Q32:C2	64,191
C₂²×C₂²⋊C₄	Direct product of C₂² and C₂²⋊C₄	32		C2^2xC2^2:C4	64,193
C₂×C₄²⋊C₂	Direct product of C₂ and C₄²⋊C₂	32		C2xC4^2:C2	64,195
C₂×C₄×D₄	Direct product of C₂×C₄ and D₄	32		C2xC4xD4	64,196
C₄×C₄○D₄	Direct product of C₄ and C₄○D₄	32		C4xC4oD4	64,198
C₂³.₃₂C₂³	5^th non-split extension by C₂³ of C₂³ acting via C₂³/C₂²=C₂	32		C2^3.32C2^3	64,200
C₂³.₃₃C₂³	6^th non-split extension by C₂³ of C₂³ acting via C₂³/C₂²=C₂	32		C2^3.33C2^3	64,201
C₂×C₄⋊D₄	Direct product of C₂ and C₄⋊D₄	32		C2xC4:D4	64,203
C₂×C₂²⋊Q₈	Direct product of C₂ and C₂²⋊Q₈	32		C2xC2^2:Q8	64,204
C₂×C₂².D₄	Direct product of C₂ and C₂².D₄	32		C2xC2^2.D4	64,205
C₂×C₄.₄D₄	Direct product of C₂ and C₄.₄D₄	32		C2xC4.4D4	64,207
C₂×C₄²⋊₂C₂	Direct product of C₂ and C₄²⋊₂C₂	32		C2xC4^2:2C2	64,209
C₂³.₃₆C₂³	9^th non-split extension by C₂³ of C₂³ acting via C₂³/C₂²=C₂	32		C2^3.36C2^3	64,210
C₂×C₄⋊₁D₄	Direct product of C₂ and C₄⋊₁D₄	32		C2xC4:1D4	64,211
C₂².₂₆C₂⁴	12^nd central stem extension by C₂² of C₂⁴	32		C2^2.26C2^4	64,213
C₂³.₃₇C₂³	10^th non-split extension by C₂³ of C₂³ acting via C₂³/C₂²=C₂	32		C2^3.37C2^3	64,214
C₂³.₃₈C₂³	11^st non-split extension by C₂³ of C₂³ acting via C₂³/C₂²=C₂	32		C2^3.38C2^3	64,217
C₂².₃₁C₂⁴	17^th central stem extension by C₂² of C₂⁴	32		C2^2.31C2^4	64,218
C₂².₃₃C₂⁴	19^th central stem extension by C₂² of C₂⁴	32		C2^2.33C2^4	64,220
C₂².₃₄C₂⁴	20^th central stem extension by C₂² of C₂⁴	32		C2^2.34C2^4	64,221
C₂².₃₅C₂⁴	21^st central stem extension by C₂² of C₂⁴	32		C2^2.35C2^4	64,222
C₂².₃₆C₂⁴	22^nd central stem extension by C₂² of C₂⁴	32		C2^2.36C2^4	64,223
C₂³.₄₁C₂³	14^th non-split extension by C₂³ of C₂³ acting via C₂³/C₂²=C₂	32		C2^3.41C2^3	64,225
D₄⋊₆D₄	2^nd semidirect product of D₄ and D₄ acting through Inn(D₄)	32		D4:6D4	64,228
Q₈⋊₅D₄	1^st semidirect product of Q₈ and D₄ acting through Inn(Q₈)	32		Q8:5D4	64,229
D₄×Q₈	Direct product of D₄ and Q₈	32		D4xQ8	64,230
Q₈⋊₆D₄	2^nd semidirect product of Q₈ and D₄ acting through Inn(Q₈)	32		Q8:6D4	64,231
C₂².₄₆C₂⁴	32^nd central stem extension by C₂² of C₂⁴	32		C2^2.46C2^4	64,233
C₂².₄₇C₂⁴	33^rd central stem extension by C₂² of C₂⁴	32		C2^2.47C2^4	64,234
D₄⋊₃Q₈	The semidirect product of D₄ and Q₈ acting through Inn(D₄)	32		D4:3Q8	64,235
C₂².₄₉C₂⁴	35^th central stem extension by C₂² of C₂⁴	32		C2^2.49C2^4	64,236
C₂².₅₀C₂⁴	36^th central stem extension by C₂² of C₂⁴	32		C2^2.50C2^4	64,237
C₂².₅₃C₂⁴	39^th central stem extension by C₂² of C₂⁴	32		C2^2.53C2^4	64,240
C₂².₅₆C₂⁴	42^nd central stem extension by C₂² of C₂⁴	32		C2^2.56C2^4	64,243
C₂².₅₇C₂⁴	43^rd central stem extension by C₂² of C₂⁴	32		C2^2.57C2^4	64,244
C₂²×M₄(2)	Direct product of C₂² and M₄(2)	32		C2^2xM4(2)	64,247
C₂×C₈○D₄	Direct product of C₂ and C₈○D₄	32		C2xC8oD4	64,248
C₂²×D₈	Direct product of C₂² and D₈	32		C2^2xD8	64,250
C₂²×SD₁₆	Direct product of C₂² and SD₁₆	32		C2^2xSD16	64,251
C₂×C₄○D₈	Direct product of C₂ and C₄○D₈	32		C2xC4oD8	64,253
C₂×C₈.C₂²	Direct product of C₂ and C₈.C₂²	32		C2xC8.C2^2	64,255
Q₈○D₈	Central product of Q₈ and D₈	32	4-	Q8oD8	64,259
D₄×C₂³	Direct product of C₂³ and D₄	32		D4xC2^3	64,261
C₂²×C₄○D₄	Direct product of C₂² and C₄○D₄	32		C2^2xC4oD4	64,263
C₂×2_-¹⁺⁴	Direct product of C₂ and 2_-¹⁺⁴	32		C2xES-(2,2)	64,265

Groups of order 96

		d	ρ	Label	ID
Q₈⋊Dic₃	The semidirect product of Q₈ and Dic₃ acting via Dic₃/C₂=S₃	32		Q8:Dic3	96,66
C₄×SL₂(𝔽₃)	Direct product of C₄ and SL₂(𝔽₃)	32		C4xSL(2,3)	96,69
C₈.A₄	The central extension by C₈ of A₄	32	2	C8.A4	96,74
C₂×CSU₂(𝔽₃)	Direct product of C₂ and CSU₂(𝔽₃)	32		C2xCSU(2,3)	96,188
C₄.S₄	2^nd non-split extension by C₄ of S₄ acting via S₄/A₄=C₂	32	4-	C4.S4	96,191
C₂²×SL₂(𝔽₃)	Direct product of C₂² and SL₂(𝔽₃)	32		C2^2xSL(2,3)	96,198
C₂×C₄.A₄	Direct product of C₂ and C₄.A₄	32		C2xC4.A4	96,200

Groups of order 128

		d	ρ	Label	ID
C₄²⋊₁C₈	1^st semidirect product of C₄² and C₈ acting via C₈/C₂=C₄	32		C4^2:1C8	128,6
C₄²⋊₆C₈	3^rd semidirect product of C₄² and C₈ acting via C₈/C₄=C₂	32		C4^2:6C8	128,8
C₂³.₂₁C₄²	3^rd non-split extension by C₂³ of C₄² acting via C₄²/C₂×C₄=C₂	32		C2^3.21C4^2	128,14
C₂⁴.₄₆D₄	1^st non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.46D4	128,16
C₄².₄Q₈	4^th non-split extension by C₄² of Q₈ acting via Q₈/C₂=C₂²	32		C4^2.4Q8	128,17
C₄².₅Q₈	5^th non-split extension by C₄² of Q₈ acting via Q₈/C₂=C₂²	32		C4^2.5Q8	128,18
C₄².₆Q₈	6^th non-split extension by C₄² of Q₈ acting via Q₈/C₂=C₂²	32		C4^2.6Q8	128,20
C₂³.₈D₈	1^st non-split extension by C₂³ of D₈ acting via D₈/C₄=C₂²	32		C2^3.8D8	128,21
C₂⁴.₂Q₈	1^st non-split extension by C₂⁴ of Q₈ acting via Q₈/C₂=C₂²	32		C2^4.2Q8	128,25
C₂³.₃₀D₈	1^st non-split extension by C₂³ of D₈ acting via D₈/D₄=C₂	32		C2^3.30D8	128,26
C₂⁴.₄₈D₄	3^rd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.48D4	128,29
C₂⁴.₃Q₈	2^nd non-split extension by C₂⁴ of Q₈ acting via Q₈/C₂=C₂²	32		C2^4.3Q8	128,30
C₄².₉Q₈	9^th non-split extension by C₄² of Q₈ acting via Q₈/C₂=C₂²	32		C4^2.9Q8	128,32
C₄².₁₀Q₈	10^th non-split extension by C₄² of Q₈ acting via Q₈/C₂=C₂²	32		C4^2.10Q8	128,35
C₂³.C₄²	2^nd non-split extension by C₂³ of C₄² acting via C₄²/C₂²=C₂²	32		C2^3.C4^2	128,37
C₂³.₈C₄²	3^rd non-split extension by C₂³ of C₄² acting via C₄²/C₂²=C₂²	32		C2^3.8C4^2	128,38
C₂³⋊C₁₆	The semidirect product of C₂³ and C₁₆ acting via C₁₆/C₄=C₄	32		C2^3:C16	128,46
C₂³.₁₅M₄(2)	2^nd non-split extension by C₂³ of M₄(2) acting via M₄(2)/C₂²=C₄	32		C2^3.15M4(2)	128,49
(C₂×D₄)⋊C₈	2^nd semidirect product of C₂×D₄ and C₈ acting via C₈/C₂=C₄	32		(C2xD4):C8	128,50
(C₂×C₄²).C₄	6^th non-split extension by C₂×C₄² of C₄ acting faithfully	32		(C2xC4^2).C4	128,51
C₂³.₁M₄(2)	1^st non-split extension by C₂³ of M₄(2) acting via M₄(2)/C₄=C₄	32	4	C2^3.1M4(2)	128,53
C₄²⋊C₈	2^nd semidirect product of C₄² and C₈ acting via C₈/C₂=C₄	32		C4^2:C8	128,56
C₄²⋊₃C₈	3^rd semidirect product of C₄² and C₈ acting via C₈/C₂=C₄	32		C4^2:3C8	128,57
C₂³.₂M₄(2)	2^nd non-split extension by C₂³ of M₄(2) acting via M₄(2)/C₄=C₄	32		C2^3.2M4(2)	128,58
C₂²⋊C₄.C₈	The non-split extension by C₂²⋊C₄ of C₈ acting via C₈/C₂=C₄	32	4	C2^2:C4.C8	128,60
C₂³.₂D₈	2^nd non-split extension by C₂³ of D₈ acting via D₈/C₂=D₄	32	8-	C2^3.2D8	128,72
C₂³.₂SD₁₆	2^nd non-split extension by C₂³ of SD₁₆ acting via SD₁₆/C₂=D₄	32	8-	C2^3.2SD16	128,74
C₂³.₄D₈	4^th non-split extension by C₂³ of D₈ acting via D₈/C₂=D₄	32		C2^3.4D8	128,76
C₂.C₂≀C₄	2^nd central stem extension by C₂ of C₂≀C₄	32		C2.C2wrC4	128,77
(C₂×C₄).D₈	4^th non-split extension by C₂×C₄ of D₈ acting via D₈/C₂=D₄	32		(C2xC4).D8	128,78
C₂².SD₃₂	1^st non-split extension by C₂² of SD₃₂ acting via SD₃₂/Q₁₆=C₂	32		C2^2.SD32	128,79
C₂³.₃₂D₈	3^rd non-split extension by C₂³ of D₈ acting via D₈/D₄=C₂	32		C2^3.32D8	128,80
C₂³.Q₁₆	1^st non-split extension by C₂³ of Q₁₆ acting via Q₁₆/C₂=D₄	32		C2^3.Q16	128,83
C₂⁴.₄D₄	4^th non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.4D4	128,84
(C₂×C₄).Q₁₆	1^st non-split extension by C₂×C₄ of Q₁₆ acting via Q₁₆/C₂=D₄	32		(C2xC4).Q16	128,85
C₂.₇C₂≀C₄	4^th central stem extension by C₂ of C₂≀C₄	32		C2.7C2wrC4	128,86
C₄².(C₂×C₄)	2^nd non-split extension by C₄² of C₂×C₄ acting faithfully	32	8-	C4^2.(C2xC4)	128,88
C₈.₂₅D₈	2^nd non-split extension by C₈ of D₈ acting via D₈/D₄=C₂	32	4-	C8.25D8	128,90
C₈.₁Q₁₆	1^st non-split extension by C₈ of Q₁₆ acting via Q₁₆/C₄=C₂²	32	4	C8.1Q16	128,98
C₁₆.C₈	1^st non-split extension by C₁₆ of C₈ acting via C₈/C₂=C₄	32	4	C16.C8	128,101
C₁₆.₃C₈	1^st non-split extension by C₁₆ of C₈ acting via C₈/C₄=C₂	32	2	C16.3C8	128,105
C₄².₂C₈	2^nd non-split extension by C₄² of C₈ acting via C₈/C₂=C₄	32		C4^2.2C8	128,107
C₄².₇C₈	4^th non-split extension by C₄² of C₈ acting via C₈/C₄=C₂	32		C4^2.7C8	128,108
M₄(2).C₈	2^nd non-split extension by M₄(2) of C₈ acting via C₈/C₄=C₂	32	4	M4(2).C8	128,110
C₈.₁₁C₄²	5^th non-split extension by C₈ of C₄² acting via C₄²/C₂×C₄=C₂	32		C8.11C4^2	128,115
C₂³.₉D₈	2^nd non-split extension by C₂³ of D₈ acting via D₈/C₄=C₂²	32	4	C2^3.9D8	128,116
C₈.₁₃C₄²	7^th non-split extension by C₈ of C₄² acting via C₄²/C₂×C₄=C₂	32	4	C8.13C4^2	128,117
C₈.C₄²	1^st non-split extension by C₈ of C₄² acting via C₄²/C₂²=C₂²	32		C8.C4^2	128,118
M₅(2).C₄	2^nd non-split extension by M₅(2) of C₄ acting via C₄/C₂=C₂	32	4	M5(2).C4	128,120
C₈.₄C₄²	4^th non-split extension by C₈ of C₄² acting via C₄²/C₂²=C₂²	32	4	C8.4C4^2	128,121
C₂⁴.₅D₄	5^th non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.5D4	128,122
C₂³.₂C₄²	2^nd non-split extension by C₂³ of C₄² acting via C₄²/C₄=C₄	32	4	C2^3.2C4^2	128,123
C₂³.₃C₄²	3^rd non-split extension by C₂³ of C₄² acting via C₄²/C₄=C₄	32	4	C2^3.3C4^2	128,124
C₂⁴.₆D₄	6^th non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.6D4	128,125
(C₂×Q₈).Q₈	2^nd non-split extension by C₂×Q₈ of Q₈ acting via Q₈/C₂=C₂²	32		(C2xQ8).Q8	128,126
(C₂²×C₈)⋊C₄	4^th semidirect product of C₂²×C₈ and C₄ acting faithfully	32	4	(C2^2xC8):C4	128,127
C₃₂⋊C₄	2^nd semidirect product of C₃₂ and C₄ acting faithfully	32	4	C32:C4	128,130
C₂³.C₁₆	The non-split extension by C₂³ of C₁₆ acting via C₁₆/C₄=C₄	32	4	C2^3.C16	128,132
(C₂×D₄).D₄	4^th non-split extension by C₂×D₄ of D₄ acting faithfully	32	8-	(C2xD4).D4	128,139
(C₂×Q₈).D₄	6^th non-split extension by C₂×Q₈ of D₄ acting faithfully	32	4-	(C2xQ8).D4	128,143
C₈⋊C₄.C₄	3^rd non-split extension by C₈⋊C₄ of C₄ acting faithfully	32	8-	C8:C4.C4	128,145
(C₄×C₈)⋊C₄	3^rd semidirect product of C₄×C₈ and C₄ acting faithfully	32	4	(C4xC8):C4	128,146
D₁₆⋊₃C₄	2^nd semidirect product of D₁₆ and C₄ acting via C₄/C₂=C₂	32	4	D16:3C4	128,150
M₆(2)⋊C₂	6^th semidirect product of M₆(2) and C₂ acting faithfully	32	4+	M6(2):C2	128,151
C₈.C₁₆	1^st non-split extension by C₈ of C₁₆ acting via C₁₆/C₈=C₂	32	2	C8.C16	128,154
C₈.Q₁₆	2^nd non-split extension by C₈ of Q₁₆ acting via Q₁₆/C₄=C₂²	32	4	C8.Q16	128,158
C₂×C₂³⋊C₈	Direct product of C₂ and C₂³⋊C₈	32		C2xC2^3:C8	128,188
C₄².₃₇₁D₄	4^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	32		C4^2.371D4	128,190
C₂³.₈M₄(2)	4^th non-split extension by C₂³ of M₄(2) acting via M₄(2)/C₄=C₂²	32		C2^3.8M4(2)	128,191
C₄².₃₉₃D₄	26^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	32		C4^2.393D4	128,192
(C₂×C₄)⋊M₄(2)	The semidirect product of C₂×C₄ and M₄(2) acting via M₄(2)/C₂²=C₄	32		(C2xC4):M4(2)	128,195
C₄².₄₂D₄	24^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.42D4	128,196
C₂³⋊M₄(2)	The semidirect product of C₂³ and M₄(2) acting via M₄(2)/C₄=C₄	32		C2^3:M4(2)	128,197
C₄².₄₃D₄	25^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.43D4	128,198
C₂³⋊C₈⋊C₂	15^th semidirect product of C₂³⋊C₈ and C₂ acting faithfully	32		C2^3:C8:C2	128,200
C₄².₃₉₅D₄	28^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	32		C4^2.395D4	128,201
C₂⁴.(C₂×C₄)	3^rd non-split extension by C₂⁴ of C₂×C₄ acting faithfully	32		C2^4.(C2xC4)	128,203
C₂⁴.₄₅(C₂×C₄)	10^th non-split extension by C₂⁴ of C₂×C₄ acting via C₂×C₄/C₂=C₂²	32		C2^4.45(C2xC4)	128,204
C₄².₃₇₂D₄	5^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	32		C4^2.372D4	128,205
C₄².₃₉₈D₄	31^st non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	32		C4^2.398D4	128,210
D₄⋊M₄(2)	1^st semidirect product of D₄ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	32		D4:M4(2)	128,218
D₄⋊₅M₄(2)	3^rd semidirect product of D₄ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	32		D4:5M4(2)	128,222
C₂×C₂².SD₁₆	Direct product of C₂ and C₂².SD₁₆	32		C2xC2^2.SD16	128,230
C₂×C₂³.₃₁D₄	Direct product of C₂ and C₂³.₃₁D₄	32		C2xC2^3.31D4	128,231
C₄².₃₇₅D₄	8^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	32		C4^2.375D4	128,232
C₂⁴.₅₃D₄	8^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.53D4	128,233
C₄².₄₀₃D₄	36^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	32		C4^2.403D4	128,234
C₄².₄₀₄D₄	37^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	32		C4^2.404D4	128,235
C₄².₅₅D₄	37^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.55D4	128,237
C₄².₅₆D₄	38^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.56D4	128,238
C₂⁴.₅₄D₄	9^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.54D4	128,239
C₂⁴.₅₅D₄	10^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.55D4	128,240
C₄².₅₇D₄	39^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.57D4	128,241
C₂⁴.₅₆D₄	11^st non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.56D4	128,242
C₂⁴.₅₇D₄	12^nd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.57D4	128,243
C₄².₅₈D₄	40^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.58D4	128,244
C₂⁴.₅₈D₄	13^rd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.58D4	128,245
C₄².₅₉D₄	41^st non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.59D4	128,246
C₄².₆₀D₄	42^nd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.60D4	128,247
C₂⁴.₅₉D₄	14^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.59D4	128,248
C₄².₆₁D₄	43^rd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.61D4	128,249
C₄².₆₂D₄	44^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.62D4	128,250
C₂⁴.₆₀D₄	15^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.60D4	128,251
C₂⁴.₆₁D₄	16^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.61D4	128,252
C₄².₆₃D₄	45^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.63D4	128,253
C₄².₄₀₇D₄	40^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	32		C4^2.407D4	128,259
C₄².₇₀D₄	52^nd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.70D4	128,265
C₄².₄₁₃D₄	46^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	32		C4^2.413D4	128,277
C₄².₈₂D₄	64^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.82D4	128,287
C₄⋊C₄.D₄	1^st non-split extension by C₄⋊C₄ of D₄ acting faithfully	32		C4:C4.D4	128,329
(C₂×C₄)⋊D₈	The semidirect product of C₂×C₄ and D₈ acting via D₈/C₂=D₄	32		(C2xC4):D8	128,330
(C₂×C₄)⋊SD₁₆	1^st semidirect product of C₂×C₄ and SD₁₆ acting via SD₁₆/C₂=D₄	32		(C2xC4):SD16	128,331
C₂³⋊₂SD₁₆	2^nd semidirect product of C₂³ and SD₁₆ acting via SD₁₆/C₂=D₄	32		C2^3:2SD16	128,333
C₂³⋊Q₁₆	The semidirect product of C₂³ and Q₁₆ acting via Q₁₆/C₂=D₄	32		C2^3:Q16	128,334
C₄⋊C₄.₆D₄	6^th non-split extension by C₄⋊C₄ of D₄ acting faithfully	32		C4:C4.6D4	128,335
Q₈⋊D₄⋊C₂	26^th semidirect product of Q₈⋊D₄ and C₂ acting faithfully	32		Q8:D4:C2	128,336
(C₂×C₄)⋊Q₁₆	The semidirect product of C₂×C₄ and Q₁₆ acting via Q₁₆/C₂=D₄	32		(C2xC4):Q16	128,337
C₂⁴.₁₂D₄	12^nd non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.12D4	128,338
C₂³.₅D₈	5^th non-split extension by C₂³ of D₈ acting via D₈/C₂=D₄	32		C2^3.5D8	128,339
C₂⁴.₁₄D₄	14^th non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.14D4	128,340
C₄⋊C₄.₁₂D₄	12^nd non-split extension by C₄⋊C₄ of D₄ acting faithfully	32		C4:C4.12D4	128,341
(C₂×C₄).₅D₈	5^th non-split extension by C₂×C₄ of D₈ acting via D₈/C₂=D₄	32		(C2xC4).5D8	128,342
(C₂×C₄).SD₁₆	7^th non-split extension by C₂×C₄ of SD₁₆ acting via SD₁₆/C₂=D₄	32		(C2xC4).SD16	128,343
C₂⁴.₁₅D₄	15^th non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.15D4	128,344
C₂⁴.₁₆D₄	16^th non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.16D4	128,345
C₂⁴.₁₇D₄	17^th non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.17D4	128,346
C₄⋊C₄.₁₈D₄	18^th non-split extension by C₄⋊C₄ of D₄ acting faithfully	32		C4:C4.18D4	128,347
C₄⋊C₄.₁₉D₄	19^th non-split extension by C₄⋊C₄ of D₄ acting faithfully	32		C4:C4.19D4	128,348
C₄⋊C₄.₂₀D₄	20^th non-split extension by C₄⋊C₄ of D₄ acting faithfully	32		C4:C4.20D4	128,349
C₂⁴.₁₈D₄	18^th non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.18D4	128,350
D₄⋊D₈	1^st semidirect product of D₄ and D₈ acting via D₈/D₄=C₂	32		D4:D8	128,351
D₄⋊₂SD₁₆	1^st semidirect product of D₄ and SD₁₆ acting via SD₁₆/D₄=C₂	32		D4:2SD16	128,361
D₄.D₈	1^st non-split extension by D₄ of D₈ acting via D₈/D₄=C₂	32		D4.D8	128,371
C₄².C₂³	1^st non-split extension by C₄² of C₂³ acting faithfully	32		C4^2.C2^3	128,387
C₄².₅C₂³	5^th non-split extension by C₄² of C₂³ acting faithfully	32		C4^2.5C2^3	128,391
C₂×C₄.₉C₄²	Direct product of C₂ and C₄.₉C₄²	32		C2xC4.9C4^2	128,462
C₂×C₄.₁₀C₄²	Direct product of C₂ and C₄.₁₀C₄²	32		C2xC4.10C4^2	128,463
C₂×C₄²⋊₆C₄	Direct product of C₂ and C₄²⋊₆C₄	32		C2xC4^2:6C4	128,464
C₂⁴.₆₃D₄	18^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.63D4	128,465
C₂⁴.₇Q₈	6^th non-split extension by C₂⁴ of Q₈ acting via Q₈/C₂=C₂²	32		C2^4.7Q8	128,470
C₂×C₂³.₉D₄	Direct product of C₂ and C₂³.₉D₄	32		C2xC2^3.9D4	128,471
C₂⁴.₁₆₂C₂³	2^nd non-split extension by C₂⁴ of C₂³ acting via C₂³/C₂=C₂²	32		C2^4.162C2^3	128,472
C₂³.₁₅C₄²	10^th non-split extension by C₂³ of C₄² acting via C₄²/C₂²=C₂²	32		C2^3.15C4^2	128,474
C₂×M₄(2)⋊₄C₄	Direct product of C₂ and M₄(2)⋊₄C₄	32		C2xM4(2):4C4	128,475
C₈.₁₆C₄²	10^th non-split extension by C₈ of C₄² acting via C₄²/C₂×C₄=C₂	32	4	C8.16C4^2	128,479
C₄×C₂³⋊C₄	Direct product of C₄ and C₂³⋊C₄	32		C4xC2^3:C4	128,486
C₄×C₄.D₄	Direct product of C₄ and C₄.D₄	32		C4xC4.D4	128,487
C₂³.₅C₄²	5^th non-split extension by C₂³ of C₄² acting via C₄²/C₄=C₄	32	4	C2^3.5C4^2	128,489
C₄×C₄≀C₂	Direct product of C₄ and C₄≀C₂	32		C4xC4wrC2	128,490
D₄.C₄²	1^st non-split extension by D₄ of C₄² acting via C₄²/C₂×C₄=C₂	32		D4.C4^2	128,491
Q₈.C₄²	2^nd non-split extension by Q₈ of C₄² acting via C₄²/C₂×C₄=C₂	32		Q8.C4^2	128,496
D₄.₃C₄²	3^rd non-split extension by D₄ of C₄² acting via C₄²/C₂×C₄=C₂	32		D4.3C4^2	128,497
C₈.₁₄C₄²	8^th non-split extension by C₈ of C₄² acting via C₄²/C₂×C₄=C₂	32		C8.14C4^2	128,504
C₈.₅C₄²	5^th non-split extension by C₈ of C₄² acting via C₄²/C₂²=C₂²	32		C8.5C4^2	128,505
C₂⁴⋊₃C₈	1^st semidirect product of C₂⁴ and C₈ acting via C₈/C₄=C₂	32		C2^4:3C8	128,511
C₂⁴.₁₆₅C₂³	5^th non-split extension by C₂⁴ of C₂³ acting via C₂³/C₂=C₂²	32		C2^4.165C2^3	128,514
C₄.C₂²≀C₂	2^nd non-split extension by C₄ of C₂²≀C₂ acting via C₂²≀C₂/C₂×D₄=C₂	32		C4.C2^2wrC2	128,516
(C₂³×C₄).C₄	20^th non-split extension by C₂³×C₄ of C₄ acting faithfully	32		(C2^3xC4).C4	128,517
C₂³.₃₅D₈	6^th non-split extension by C₂³ of D₈ acting via D₈/D₄=C₂	32		C2^3.35D8	128,518
C₂⁴.₆₆D₄	21^st non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.66D4	128,521
2₊¹⁺⁴⋊₂C₄	1^st semidirect product of 2₊¹⁺⁴ and C₄ acting via C₄/C₂=C₂	32		ES+(2,2):2C4	128,522
2₊¹⁺⁴.₂C₄	The non-split extension by 2₊¹⁺⁴ of C₄ acting via C₄/C₂=C₂	32	4	ES+(2,2).2C4	128,523
2₊¹⁺⁴⋊₃C₄	2^nd semidirect product of 2₊¹⁺⁴ and C₄ acting via C₄/C₂=C₂	32		ES+(2,2):3C4	128,524
2_-¹⁺⁴⋊₂C₄	1^st semidirect product of 2_-¹⁺⁴ and C₄ acting via C₄/C₂=C₂	32		ES-(2,2):2C4	128,525
2₊¹⁺⁴⋊₄C₄	3^rd semidirect product of 2₊¹⁺⁴ and C₄ acting via C₄/C₂=C₂	32	4	ES+(2,2):4C4	128,526
(C₂²×Q₈)⋊C₄	6^th semidirect product of C₂²×Q₈ and C₄ acting faithfully	32	8-	(C2^2xQ8):C4	128,528
C₂⁴.₁₆₇C₂³	7^th non-split extension by C₂⁴ of C₂³ acting via C₂³/C₂=C₂²	32		C2^4.167C2^3	128,531
C₄².₉₆D₄	78^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.96D4	128,532
C₄².₁₀₂D₄	84^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.102D4	128,538
C₂⁴.₁₉Q₈	3^rd non-split extension by C₂⁴ of Q₈ acting via Q₈/C₄=C₂	32		C2^4.19Q8	128,542
C₂⁴.₉Q₈	8^th non-split extension by C₂⁴ of Q₈ acting via Q₈/C₂=C₂²	32		C2^4.9Q8	128,543
(C₂×D₄).₂₄Q₈	5^th non-split extension by C₂×D₄ of Q₈ acting via Q₈/C₄=C₂	32	4	(C2xD4).24Q8	128,544
(C₂×C₈).₁₀₃D₄	71^st non-split extension by C₂×C₈ of D₄ acting via D₄/C₂=C₂²	32	4	(C2xC8).103D4	128,545
C₈○D₄⋊C₄	1^st semidirect product of C₈○D₄ and C₄ acting via C₄/C₂=C₂	32	4	C8oD4:C4	128,546
C₂⁴.₁₆₉C₂³	9^th non-split extension by C₂⁴ of C₂³ acting via C₂³/C₂=C₂²	32		C2^4.169C2^3	128,552
(C₂²×C₄).₂₇₅D₄	160^th non-split extension by C₂²×C₄ of D₄ acting via D₄/C₂=C₂²	32		(C2^2xC4).275D4	128,553
(C₂²×C₄).₂₇₆D₄	161^st non-split extension by C₂²×C₄ of D₄ acting via D₄/C₂=C₂²	32		(C2^2xC4).276D4	128,554
C₂⁴.₇₀D₄	25^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.70D4	128,558
(C₂×Q₈).₂₁₁D₄	19^th non-split extension by C₂×Q₈ of D₄ acting via D₄/C₂²=C₂	32	8-	(C2xQ8).211D4	128,562
C₈.(C₄⋊C₄)	4^th non-split extension by C₈ of C₄⋊C₄ acting via C₄⋊C₄/C₂²=C₂²	32	4	C8.(C4:C4)	128,565
C₂⁴.₁₀Q₈	9^th non-split extension by C₂⁴ of Q₈ acting via Q₈/C₂=C₂²	32		C2^4.10Q8	128,587
C₂⁴.₂₁D₄	21^st non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.21D4	128,588
C₄.₁₀D₄⋊₂C₄	1^st semidirect product of C₄.₁₀D₄ and C₄ acting via C₄/C₂=C₂	32		C4.10D4:2C4	128,589
M₄(2).₄₀D₄	4^th non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	32	4	M4(2).40D4	128,590
C₄≀C₂⋊C₄	1^st semidirect product of C₄≀C₂ and C₄ acting via C₄/C₂=C₂	32		C4wrC2:C4	128,591
C₄²⋊₉(C₂×C₄)	4^th semidirect product of C₄² and C₂×C₄ acting via C₂×C₄/C₂=C₂²	32		C4^2:9(C2xC4)	128,592
M₄(2).₄₂D₄	6^th non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	32		M4(2).42D4	128,598
C₂⁴.₂₂D₄	22^nd non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.22D4	128,599
(C₂×D₄).Q₈	9^th non-split extension by C₂×D₄ of Q₈ acting via Q₈/C₂=C₂²	32	4	(C2xD4).Q8	128,600
C₂⁴.₇₂D₄	27^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.72D4	128,603
M₄(2).₄₃D₄	7^th non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	32		M4(2).43D4	128,608
M₄(2).₄₄D₄	8^th non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	32	4	M4(2).44D4	128,613
C₈.C₂²⋊C₄	2^nd semidirect product of C₈.C₂² and C₄ acting via C₄/C₂=C₂	32		C8.C2^2:C4	128,614
C₈⋊C₂²⋊C₄	2^nd semidirect product of C₈⋊C₂² and C₄ acting via C₄/C₂=C₂	32		C8:C2^2:C4	128,615
C₂⁴.₂₃D₄	23^rd non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.23D4	128,617
C₄⋊Q₈⋊₁₅C₄	10^th semidirect product of C₄⋊Q₈ and C₄ acting via C₄/C₂=C₂	32		C4:Q8:15C4	128,618
C₄.₄D₄⋊₁₃C₄	7^th semidirect product of C₄.₄D₄ and C₄ acting via C₄/C₂=C₂	32		C4.4D4:13C4	128,620
C₂⁴.₂₆D₄	26^th non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.26D4	128,622
C₄²⋊₇D₄	1^st semidirect product of C₄² and D₄ acting via D₄/C₂=C₂²	32		C4^2:7D4	128,629
C₂⁴.₁₇₄C₂³	14^th non-split extension by C₂⁴ of C₂³ acting via C₂³/C₂=C₂²	32		C2^4.174C2^3	128,631
M₄(2)⋊₂₀D₄	7^th semidirect product of M₄(2) and D₄ acting via D₄/C₂²=C₂	32		M4(2):20D4	128,632
M₄(2).₄₅D₄	9^th non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	32		M4(2).45D4	128,633
M₄(2).₄₆D₄	10^th non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	32	8-	M4(2).46D4	128,634
C₄².₆D₄	6^th non-split extension by C₄² of D₄ acting faithfully	32	8-	C4^2.6D4	128,637
M₄(2).₄₈D₄	12^nd non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	32		M4(2).48D4	128,639
C₄.(C₄×D₄)	5^th non-split extension by C₄ of C₄×D₄ acting via C₄×D₄/C₄²=C₂	32	8-	C4.(C4xD4)	128,641
C₄².₇D₄	7^th non-split extension by C₄² of D₄ acting faithfully	32	8-	C4^2.7D4	128,644
M₄(2).₅₀D₄	14^th non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	32	8-	M4(2).50D4	128,647
M₄(2).₃Q₈	1^st non-split extension by M₄(2) of Q₈ acting via Q₈/C₄=C₂	32		M4(2).3Q8	128,654
M₄(2).₂₄D₄	5^th non-split extension by M₄(2) of D₄ acting via D₄/C₄=C₂	32		M4(2).24D4	128,661
C₄.D₄⋊₃C₄	2^nd semidirect product of C₄.D₄ and C₄ acting via C₄/C₂=C₂	32		C4.D4:3C4	128,663
C₄².₄₂₈D₄	61^st non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	32		C4^2.428D4	128,669
C₄².₁₀₇D₄	89^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.107D4	128,670
C₄².₆₂Q₈	22^nd non-split extension by C₄² of Q₈ acting via Q₈/C₄=C₂	32		C4^2.62Q8	128,677
C₄².₂₈Q₈	28^th non-split extension by C₄² of Q₈ acting via Q₈/C₂=C₂²	32		C4^2.28Q8	128,678
M₄(2).₂₇D₄	8^th non-split extension by M₄(2) of D₄ acting via D₄/C₄=C₂	32	4	M4(2).27D4	128,685
C₄³⋊C₂	7^th semidirect product of C₄³ and C₂ acting faithfully	32		C4^3:C2	128,694
C₄²⋊₈D₄	2^nd semidirect product of C₄² and D₄ acting via D₄/C₂=C₂²	32		C4^2:8D4	128,695
C₂⁴.₁₇₅C₂³	15^th non-split extension by C₂⁴ of C₂³ acting via C₂³/C₂=C₂²	32		C2^4.175C2^3	128,696
M₄(2)⋊₁₂D₄	6^th semidirect product of M₄(2) and D₄ acting via D₄/C₄=C₂	32		M4(2):12D4	128,697
C₄².₁₁₅D₄	97^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.115D4	128,699
C₄².₃₂₆D₄	22^nd non-split extension by C₄² of D₄ acting via D₄/C₄=C₂	32		C4^2.326D4	128,706
C₄².₁₁₆D₄	98^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.116D4	128,707
M₄(2).₃₀D₄	11^st non-split extension by M₄(2) of D₄ acting via D₄/C₄=C₂	32	4	M4(2).30D4	128,708
M₄(2).₃₁D₄	12^nd non-split extension by M₄(2) of D₄ acting via D₄/C₄=C₂	32		M4(2).31D4	128,709
M₄(2).₃₂D₄	13^rd non-split extension by M₄(2) of D₄ acting via D₄/C₄=C₂	32		M4(2).32D4	128,710
M₄(2)⋊₁₃D₄	7^th semidirect product of M₄(2) and D₄ acting via D₄/C₄=C₂	32		M4(2):13D4	128,712
M₄(2)⋊₇Q₈	5^th semidirect product of M₄(2) and Q₈ acting via Q₈/C₄=C₂	32		M4(2):7Q8	128,718
C₄²⋊₁₆Q₈	3^rd semidirect product of C₄² and Q₈ acting via Q₈/C₄=C₂	32		C4^2:16Q8	128,726
C₄²⋊Q₈	1^st semidirect product of C₄² and Q₈ acting via Q₈/C₂=C₂²	32		C4^2:Q8	128,727
C₂⁴.₁₇₆C₂³	16^th non-split extension by C₂⁴ of C₂³ acting via C₂³/C₂=C₂²	32		C2^4.176C2^3	128,728
C₄².₁₂₉D₄	111^st non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.129D4	128,735
C₄²⋊₁₀D₄	4^th semidirect product of C₄² and D₄ acting via D₄/C₂=C₂²	32		C4^2:10D4	128,736
C₄².₁₃₀D₄	112^nd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.130D4	128,737
M₄(2)⋊D₄	3^rd semidirect product of M₄(2) and D₄ acting via D₄/C₂=C₂²	32		M4(2):D4	128,738
M₄(2)⋊₄D₄	4^th semidirect product of M₄(2) and D₄ acting via D₄/C₂=C₂²	32		M4(2):4D4	128,739
M₄(2).D₄	3^rd non-split extension by M₄(2) of D₄ acting via D₄/C₂=C₂²	32	8-	M4(2).D4	128,741
(C₂×C₈).₂D₄	2^nd non-split extension by C₂×C₈ of D₄ acting faithfully	32	4	(C2xC8).2D4	128,749
M₄(2).₄D₄	4^th non-split extension by M₄(2) of D₄ acting via D₄/C₂=C₂²	32		M4(2).4D4	128,750
M₄(2).₅D₄	5^th non-split extension by M₄(2) of D₄ acting via D₄/C₂=C₂²	32		M4(2).5D4	128,751
C₂⁴.₃₁D₄	31^st non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.31D4	128,754
(C₂×D₄)⋊₂Q₈	2^nd semidirect product of C₂×D₄ and Q₈ acting via Q₈/C₂=C₂²	32		(C2xD4):2Q8	128,759
(C₂×Q₈)⋊₂Q₈	2^nd semidirect product of C₂×Q₈ and Q₈ acting via Q₈/C₂=C₂²	32		(C2xQ8):2Q8	128,760
C₂⁴.₁₈₀C₂³	20^th non-split extension by C₂⁴ of C₂³ acting via C₂³/C₂=C₂²	32		C2^4.180C2^3	128,762
M₄(2)⋊₆D₄	6^th semidirect product of M₄(2) and D₄ acting via D₄/C₂=C₂²	32		M4(2):6D4	128,769
M₄(2).₇D₄	7^th non-split extension by M₄(2) of D₄ acting via D₄/C₂=C₂²	32		M4(2).7D4	128,770
C₄²⋊₁₁D₄	5^th semidirect product of C₄² and D₄ acting via D₄/C₂=C₂²	32		C4^2:11D4	128,771
C₄²⋊₁₂D₄	6^th semidirect product of C₄² and D₄ acting via D₄/C₂=C₂²	32		C4^2:12D4	128,772
C₂⁴.₃₃D₄	33^rd non-split extension by C₂⁴ of D₄ acting faithfully	32		C2^4.33D4	128,776
C₄⋊C₄.₉₆D₄	51^st non-split extension by C₄⋊C₄ of D₄ acting via D₄/C₂=C₂²	32		C4:C4.96D4	128,777
C₄⋊C₄.₉₇D₄	52^nd non-split extension by C₄⋊C₄ of D₄ acting via D₄/C₂=C₂²	32		C4:C4.97D4	128,778
M₄(2).₉D₄	9^th non-split extension by M₄(2) of D₄ acting via D₄/C₂=C₂²	32	8-	M4(2).9D4	128,781
M₄(2).₁₀D₄	10^th non-split extension by M₄(2) of D₄ acting via D₄/C₂=C₂²	32		M4(2).10D4	128,783
C₂²⋊C₄.₇D₄	5^th non-split extension by C₂²⋊C₄ of D₄ acting via D₄/C₂=C₂²	32	4	C2^2:C4.7D4	128,785
M₄(2)⋊Q₈	1^st semidirect product of M₄(2) and Q₈ acting via Q₈/C₂=C₂²	32		M4(2):Q8	128,792
C₄²⋊₃Q₈	3^rd semidirect product of C₄² and Q₈ acting via Q₈/C₂=C₂²	32		C4^2:3Q8	128,793
C₂⁴.₁₈₂C₂³	22^nd non-split extension by C₂⁴ of C₂³ acting via C₂³/C₂=C₂²	32		C2^4.182C2^3	128,794
M₄(2).₁₂D₄	12^nd non-split extension by M₄(2) of D₄ acting via D₄/C₂=C₂²	32		M4(2).12D4	128,795
M₄(2).₁₅D₄	15^th non-split extension by M₄(2) of D₄ acting via D₄/C₂=C₂²	32	8-	M4(2).15D4	128,802
C₄².₉D₄	9^th non-split extension by C₄² of D₄ acting faithfully	32	4	C4^2.9D4	128,812
(C₂×C₈).₆D₄	6^th non-split extension by C₂×C₈ of D₄ acting faithfully	32	8-	(C2xC8).6D4	128,814
C₄².₁₀D₄	10^th non-split extension by C₄² of D₄ acting faithfully	32	4	C4^2.10D4	128,830
C₂²⋊C₄.Q₈	1^st non-split extension by C₂²⋊C₄ of Q₈ acting via Q₈/C₂=C₂²	32	4	C2^2:C4.Q8	128,835
C₂×C₁₆⋊C₄	Direct product of C₂ and C₁₆⋊C₄	32		C2xC16:C4	128,841
C₈.₂₃C₄²	4^th central extension by C₈ of C₄²	32	4	C8.23C4^2	128,842
C₂⁴.₅C₈	2^nd non-split extension by C₂⁴ of C₈ acting via C₈/C₄=C₂	32		C2^4.5C8	128,844
C₂×C₂³.C₈	Direct product of C₂ and C₂³.C₈	32		C2xC2^3.C8	128,846
M₅(2).₁₉C₂²	6^th non-split extension by M₅(2) of C₂² acting via C₂²/C₂=C₂	32	4	M5(2).19C2^2	128,847
M₅(2)⋊₁₂C₂²	8^th semidirect product of M₅(2) and C₂² acting via C₂²/C₂=C₂	32	4	M5(2):12C2^2	128,849
C₂×C₂³.D₄	Direct product of C₂ and C₂³.D₄	32		C2xC2^3.D4	128,851
C₂³.(C₂×D₄)	6^th non-split extension by C₂³ of C₂×D₄ acting via C₂×D₄/C₂=D₄	32	8-	C2^3.(C2xD4)	128,855
C₂×C₄²⋊₃C₄	Direct product of C₂ and C₄²⋊₃C₄	32		C2xC4^2:3C4	128,857
C₄⋊Q₈⋊C₄	5^th semidirect product of C₄⋊Q₈ and C₄ acting faithfully	32	8-	C4:Q8:C4	128,861
C₂×C₄².C₄	Direct product of C₂ and C₄².C₄	32		C2xC4^2.C4	128,862
C₂×C₄².₃C₄	Direct product of C₂ and C₄².₃C₄	32		C2xC4^2.3C4	128,863
C₄⋊Q₈.C₄	5^th non-split extension by C₄⋊Q₈ of C₄ acting faithfully	32	8-	C4:Q8.C4	128,865
(C₂×D₄).₁₃₇D₄	99^th non-split extension by C₂×D₄ of D₄ acting via D₄/C₂=C₂²	32	8-	(C2xD4).137D4	128,867
C₂³.₄₀D₈	11^st non-split extension by C₂³ of D₈ acting via D₈/D₄=C₂	32		C2^3.40D8	128,872
C₂³.₂₀SD₁₆	10^th non-split extension by C₂³ of SD₁₆ acting via SD₁₆/C₄=C₂²	32	4	C2^3.20SD16	128,875
C₂×D₈⋊₂C₄	Direct product of C₂ and D₈⋊₂C₄	32		C2xD8:2C4	128,876
C₂³.₁₃D₈	6^th non-split extension by C₂³ of D₈ acting via D₈/C₄=C₂²	32	4	C2^3.13D8	128,877
C₂×M₅(2)⋊C₂	Direct product of C₂ and M₅(2)⋊C₂	32		C2xM5(2):C2	128,878
C₂³.₂₁SD₁₆	11^st non-split extension by C₂³ of SD₁₆ acting via SD₁₆/C₄=C₂²	32	4	C2^3.21SD16	128,880
C₂×C₈.C₈	Direct product of C₂ and C₈.C₈	32		C2xC8.C8	128,884
M₄(2).₁C₈	1^st non-split extension by M₄(2) of C₈ acting via C₈/C₄=C₂	32	4	M4(2).1C8	128,885
C₂×C₈.Q₈	Direct product of C₂ and C₈.Q₈	32		C2xC8.Q8	128,886
M₅(2)⋊₃C₄	3^rd semidirect product of M₅(2) and C₄ acting via C₄/C₂=C₂	32	4	M5(2):3C4	128,887
M₅(2).₁C₄	1^st non-split extension by M₅(2) of C₄ acting via C₄/C₂=C₂	32	4	M5(2).1C4	128,893
C₈.₁₉M₄(2)	7^th non-split extension by C₈ of M₄(2) acting via M₄(2)/C₂×C₄=C₂	32	4	C8.19M4(2)	128,898
C₁₆○D₈	Central product of C₁₆ and D₈	32	2	C16oD8	128,902
D₈.C₈	The non-split extension by D₈ of C₈ acting via C₈/C₄=C₂	32	4	D8.C8	128,903
C₈○D₁₆	Central product of C₈ and D₁₆	32	2	C8oD16	128,910
D₁₆⋊₅C₄	4^th semidirect product of D₁₆ and C₄ acting via C₄/C₂=C₂	32	4	D16:5C4	128,911
Q₃₂⋊C₄	The semidirect product of Q₃₂ and C₄ acting faithfully	32	8-	Q32:C4	128,912
D₈⋊₇D₄	1^st semidirect product of D₈ and D₄ acting via D₄/C₂²=C₂	32		D8:7D4	128,916
D₈.₉D₄	1^st non-split extension by D₈ of D₄ acting via D₄/C₂²=C₂	32		D8.9D4	128,919
D₈.D₄	1^st non-split extension by D₈ of D₄ acting via D₄/C₂=C₂²	32	8-	D8.D4	128,923
Q₁₆.₁₀D₄	3^rd non-split extension by Q₁₆ of D₄ acting via D₄/C₂²=C₂	32	4+	Q16.10D4	128,924
Q₁₆.D₄	2^nd non-split extension by Q₁₆ of D₄ acting via D₄/C₂=C₂²	32	4	Q16.D4	128,925
D₈.₃D₄	3^rd non-split extension by D₈ of D₄ acting via D₄/C₂=C₂²	32	4	D8.3D4	128,926
C₄².₁₄D₄	14^th non-split extension by C₄² of D₄ acting faithfully	32	8-	C4^2.14D4	128,933
C₄².₁₆D₄	16^th non-split extension by C₄² of D₄ acting faithfully	32	8-	C4^2.16D4	128,935
C₈.₃D₈	3^rd non-split extension by C₈ of D₈ acting via D₈/C₄=C₂²	32	4	C8.3D8	128,944
C₈.₅D₈	5^th non-split extension by C₈ of D₈ acting via D₈/C₄=C₂²	32	4-	C8.5D8	128,946
D₄.₃D₈	3^rd non-split extension by D₄ of D₈ acting via D₈/C₈=C₂	32	4+	D4.3D8	128,953
D₄.₅D₈	5^th non-split extension by D₄ of D₈ acting via D₈/C₈=C₂	32	4	D4.5D8	128,955
D₈.₂Q₈	2^nd non-split extension by D₈ of Q₈ acting via Q₈/C₄=C₂	32	4	D8.2Q8	128,963
C₂³.₁₀SD₁₆	10^th non-split extension by C₂³ of SD₁₆ acting via SD₁₆/C₂=D₄	32	8-	C2^3.10SD16	128,971
C₃₂⋊C₂²	The semidirect product of C₃₂ and C₂² acting faithfully	32	4+	C32:C2^2	128,995
C₂³⋊C₄²	2^nd semidirect product of C₂³ and C₄² acting via C₄²/C₂²=C₂²	32		C2^3:C4^2	128,1005
C₂×C₂⁴⋊₃C₄	Direct product of C₂ and C₂⁴⋊₃C₄	32		C2xC2^4:3C4	128,1009
C₂⁵.₈₅C₂²	6^th non-split extension by C₂⁵ of C₂² acting via C₂²/C₂=C₂	32		C2^5.85C2^2	128,1012
C₄×C₂²≀C₂	Direct product of C₄ and C₂²≀C₂	32		C4xC2^2wrC2	128,1031
C₂⁴.₉₀D₄	45^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.90D4	128,1040
C₂³.₁₉₁C₂⁴	44^th central extension by C₂³ of C₂⁴	32		C2^3.191C2^4	128,1041
C₂³.₁₉₄C₂⁴	47^th central extension by C₂³ of C₂⁴	32		C2^3.194C2^4	128,1044
C₂⁴.₉₁D₄	46^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.91D4	128,1047
C₂³.₂₀₃C₂⁴	56^th central extension by C₂³ of C₂⁴	32		C2^3.203C2^4	128,1053
D₄×C₂²⋊C₄	Direct product of D₄ and C₂²⋊C₄	32		D4xC2^2:C4	128,1070
C₂³.₂₂₄C₂⁴	77^th central extension by C₂³ of C₂⁴	32		C2^3.224C2^4	128,1074
C₂³.₂₄₀C₂⁴	93^rd central extension by C₂³ of C₂⁴	32		C2^3.240C2^4	128,1090
C₂³.₂₅₇C₂⁴	110^th central extension by C₂³ of C₂⁴	32		C2^3.257C2^4	128,1107
C₂⁴⋊₇D₄	2^nd semidirect product of C₂⁴ and D₄ acting via D₄/C₂=C₂²	32		C2^4:7D4	128,1135
C₂³.₃₀₄C₂⁴	21^st central stem extension by C₂³ of C₂⁴	32		C2^3.304C2^4	128,1136
C₂⁴.₉₄D₄	49^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.94D4	128,1137
C₂³.₃₀₈C₂⁴	25^th central stem extension by C₂³ of C₂⁴	32		C2^3.308C2^4	128,1140
C₂⁴⋊₈D₄	3^rd semidirect product of C₂⁴ and D₄ acting via D₄/C₂=C₂²	32		C2^4:8D4	128,1142
C₂³.₃₁₁C₂⁴	28^th central stem extension by C₂³ of C₂⁴	32		C2^3.311C2^4	128,1143
C₂⁴.₉₅D₄	50^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.95D4	128,1144
C₂³.₃₁₈C₂⁴	35^th central stem extension by C₂³ of C₂⁴	32		C2^3.318C2^4	128,1150
C₂³.₃₂₄C₂⁴	41^st central stem extension by C₂³ of C₂⁴	32		C2^3.324C2^4	128,1156
C₂³.₃₃₃C₂⁴	50^th central stem extension by C₂³ of C₂⁴	32		C2^3.333C2^4	128,1165
C₂³.₃₃₅C₂⁴	52^nd central stem extension by C₂³ of C₂⁴	32		C2^3.335C2^4	128,1167
C₂⁴⋊₄Q₈	3^rd semidirect product of C₂⁴ and Q₈ acting via Q₈/C₂=C₂²	32		C2^4:4Q8	128,1169
C₂³.₃₇₂C₂⁴	89^th central stem extension by C₂³ of C₂⁴	32		C2^3.372C2^4	128,1204
C₂³.₃₈₀C₂⁴	97^th central stem extension by C₂³ of C₂⁴	32		C2^3.380C2^4	128,1212
C₂³.₃₈₂C₂⁴	99^th central stem extension by C₂³ of C₂⁴	32		C2^3.382C2^4	128,1214
C₂⁴.₉₆D₄	51^st non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.96D4	128,1215
C₂³.₄₃₄C₂⁴	151^st central stem extension by C₂³ of C₂⁴	32		C2^3.434C2^4	128,1266
C₂³.₄₃₉C₂⁴	156^th central stem extension by C₂³ of C₂⁴	32		C2^3.439C2^4	128,1271
C₂³.₄₆₁C₂⁴	178^th central stem extension by C₂³ of C₂⁴	32		C2^3.461C2^4	128,1293
C₂⁴⋊₉D₄	4^th semidirect product of C₂⁴ and D₄ acting via D₄/C₂=C₂²	32		C2^4:9D4	128,1345
C₂⁴⋊₁₀D₄	5^th semidirect product of C₂⁴ and D₄ acting via D₄/C₂=C₂²	32		C2^4:10D4	128,1349
C₂⁴.₉₇D₄	52^nd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.97D4	128,1354
C₂⁴⋊₅Q₈	4^th semidirect product of C₂⁴ and Q₈ acting via Q₈/C₂=C₂²	32		C2^4:5Q8	128,1358
C₂³.₅₆₈C₂⁴	285^th central stem extension by C₂³ of C₂⁴	32		C2^3.568C2^4	128,1400
C₂³.₅₆₉C₂⁴	286^th central stem extension by C₂³ of C₂⁴	32		C2^3.569C2^4	128,1401
C₂³.₅₇₀C₂⁴	287^th central stem extension by C₂³ of C₂⁴	32		C2^3.570C2^4	128,1402
C₂³.₅₇₈C₂⁴	295^th central stem extension by C₂³ of C₂⁴	32		C2^3.578C2^4	128,1410
C₂⁵⋊C₂²	2^nd semidirect product of C₂⁵ and C₂² acting faithfully	32		C2^5:C2^2	128,1411
C₂³.₅₈₄C₂⁴	301^st central stem extension by C₂³ of C₂⁴	32		C2^3.584C2^4	128,1416
C₂³.₅₈₅C₂⁴	302^nd central stem extension by C₂³ of C₂⁴	32		C2^3.585C2^4	128,1417
C₂³.₅₉₇C₂⁴	314^th central stem extension by C₂³ of C₂⁴	32		C2^3.597C2^4	128,1429
C₂³.₆₃₅C₂⁴	352^nd central stem extension by C₂³ of C₂⁴	32		C2^3.635C2^4	128,1467
C₂³.₆₃₆C₂⁴	353^rd central stem extension by C₂³ of C₂⁴	32		C2^3.636C2^4	128,1468
C₂⁴⋊₁₁D₄	6^th semidirect product of C₂⁴ and D₄ acting via D₄/C₂=C₂²	32		C2^4:11D4	128,1544
C₂⁴⋊₆Q₈	5^th semidirect product of C₂⁴ and Q₈ acting via Q₈/C₂=C₂²	32		C2^4:6Q8	128,1572
C₂⁴.₁₅Q₈	14^th non-split extension by C₂⁴ of Q₈ acting via Q₈/C₂=C₂²	32		C2^4.15Q8	128,1574
C₂⁴⋊₁₃D₄	1^st semidirect product of C₂⁴ and D₄ acting via D₄/C₄=C₂	32		C2^4:13D4	128,1579
C₂⁴⋊₈Q₈	1^st semidirect product of C₂⁴ and Q₈ acting via Q₈/C₄=C₂	32		C2^4:8Q8	128,1580
C₂⁴.₁₆₆D₄	21^st non-split extension by C₂⁴ of D₄ acting via D₄/C₂²=C₂	32		C2^4.166D4	128,1581
M₄(2)○₂M₄(2)	Central product of M₄(2) and M₄(2)	32		M4(2)o2M4(2)	128,1605
C₂×C₂⁴.₄C₄	Direct product of C₂ and C₂⁴.₄C₄	32		C2xC2^4.4C4	128,1609
C₂⁴.₇₃(C₂×C₄)	38^th non-split extension by C₂⁴ of C₂×C₄ acting via C₂×C₄/C₂=C₂²	32		C2^4.73(C2xC4)	128,1611
D₄○(C₂²⋊C₈)	Central product of D₄ and C₂²⋊C₈	32		D4o(C2^2:C8)	128,1612
C₂²×C₂³⋊C₄	Direct product of C₂² and C₂³⋊C₄	32		C2^2xC2^3:C4	128,1613
C₂×C₂³.C₂³	Direct product of C₂ and C₂³.C₂³	32		C2xC2^3.C2^3	128,1614
C₂³.₄C₂⁴	4^th non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	32	8-	C2^3.4C2^4	128,1616
C₂²×C₄.D₄	Direct product of C₂² and C₄.D₄	32		C2^2xC4.D4	128,1617
C₂×M₄(2).₈C₂²	Direct product of C₂ and M₄(2).₈C₂²	32		C2xM4(2).8C2^2	128,1619
M₄(2).₂₅C₂³	7^th non-split extension by M₄(2) of C₂³ acting via C₂³/C₂²=C₂	32	8-	M4(2).25C2^3	128,1621
C₂×C₂³.₃₇D₄	Direct product of C₂ and C₂³.₃₇D₄	32		C2xC2^3.37D4	128,1625
C₂⁴.₉₈D₄	53^rd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.98D4	128,1628
2₊¹⁺⁴⋊₅C₄	4^th semidirect product of 2₊¹⁺⁴ and C₄ acting via C₄/C₂=C₂	32		ES+(2,2):5C4	128,1629
C₂²×C₄≀C₂	Direct product of C₂² and C₄≀C₂	32		C2^2xC4wrC2	128,1631
C₂×C₄²⋊C₂²	Direct product of C₂ and C₄²⋊C₂²	32		C2xC4^2:C2^2	128,1632
C₄².₂₅₇C₂³	118^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.257C2^3	128,1637
C₂⁴.₁₀₀D₄	55^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.100D4	128,1643
C₂×M₄(2).C₄	Direct product of C₂ and M₄(2).C₄	32		C2xM4(2).C4	128,1647
M₄(2).₂₉C₂³	11^st non-split extension by M₄(2) of C₂³ acting via C₂³/C₂²=C₂	32	4	M4(2).29C2^3	128,1648
C₄².₆₇₇C₂³	92^nd non-split extension by C₄² of C₂³ acting via C₂³/C₂²=C₂	32		C4^2.677C2^3	128,1652
C₄².₂₅₉C₂³	120^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.259C2^3	128,1653
C₄².₂₆₂C₂³	123^rd non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.262C2^3	128,1656
C₄².₂₆₄C₂³	125^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.264C2^3	128,1661
C₄².₂₆₅C₂³	126^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.265C2^3	128,1662
M₄(2)⋊₂₂D₄	1^st semidirect product of M₄(2) and D₄ acting through Inn(M₄(2))	32		M4(2):22D4	128,1665
D₄×M₄(2)	Direct product of D₄ and M₄(2)	32		D4xM4(2)	128,1666
C₄×C₈⋊C₂²	Direct product of C₄ and C₈⋊C₂²	32		C4xC8:C2^2	128,1676
C₄².₂₇₅C₂³	136^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.275C2^3	128,1678
C₄².₂₇₇C₂³	138^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.277C2^3	128,1680
C₄².₂₇₈C₂³	139^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.278C2^3	128,1681
C₂×C₈○D₈	Direct product of C₂ and C₈○D₈	32		C2xC8oD8	128,1685
C₂×C₈.₂₆D₄	Direct product of C₂ and C₈.₂₆D₄	32		C2xC8.26D4	128,1686
C₄².₂₈₃C₂³	144^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32	4	C4^2.283C2^3	128,1687
M₄(2)○D₈	Central product of M₄(2) and D₈	32	4	M4(2)oD8	128,1689
C₄².₆₉₁C₂³	106^th non-split extension by C₄² of C₂³ acting via C₂³/C₂²=C₂	32		C4^2.691C2^3	128,1704
C₂³⋊₃M₄(2)	2^nd semidirect product of C₂³ and M₄(2) acting via M₄(2)/C₄=C₂²	32		C2^3:3M4(2)	128,1705
D₄⋊₇M₄(2)	2^nd semidirect product of D₄ and M₄(2) acting through Inn(D₄)	32		D4:7M4(2)	128,1706
C₄².₆₉₃C₂³	108^th non-split extension by C₄² of C₂³ acting via C₂³/C₂²=C₂	32		C4^2.693C2^3	128,1707
C₄².₂₉₇C₂³	158^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.297C2^3	128,1708
C₄².₂₉₈C₂³	159^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.298C2^3	128,1709
C₄².₂₉₉C₂³	160^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.299C2^3	128,1710
C₂×C₂²⋊D₈	Direct product of C₂ and C₂²⋊D₈	32		C2xC2^2:D8	128,1728
C₂×C₂²⋊SD₁₆	Direct product of C₂ and C₂²⋊SD₁₆	32		C2xC2^2:SD16	128,1729
C₂⁴.₁₀₃D₄	58^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.103D4	128,1734
C₂⁴.₁₇₈D₄	33^rd non-split extension by C₂⁴ of D₄ acting via D₄/C₂²=C₂	32		C2^4.178D4	128,1736
C₂⁴.₁₀₄D₄	59^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.104D4	128,1737
C₂⁴.₁₀₅D₄	60^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.105D4	128,1738
C₂⁴.₁₀₆D₄	61^st non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.106D4	128,1739
C₄○D₄⋊D₄	1^st semidirect product of C₄○D₄ and D₄ acting via D₄/C₂=C₂²	32		C4oD4:D4	128,1740
D₄.(C₂×D₄)	8^th non-split extension by D₄ of C₂×D₄ acting via C₂×D₄/C₂³=C₂	32		D4.(C2xD4)	128,1741
(C₂×Q₈)⋊₁₆D₄	12^nd semidirect product of C₂×Q₈ and D₄ acting via D₄/C₂=C₂²	32		(C2xQ8):16D4	128,1742
(C₂×D₄)⋊₂₁D₄	17^th semidirect product of C₂×D₄ and D₄ acting via D₄/C₂=C₂²	32		(C2xD4):21D4	128,1744
C₂×D₄.₉D₄	Direct product of C₂ and D₄.₉D₄	32		C2xD4.9D4	128,1747
C₂×D₄.₈D₄	Direct product of C₂ and D₄.₈D₄	32		C2xD4.8D4	128,1748
C₂×D₄.₁₀D₄	Direct product of C₂ and D₄.₁₀D₄	32		C2xD4.10D4	128,1749
M₄(2).C₂³	4^th non-split extension by M₄(2) of C₂³ acting via C₂³/C₂=C₂²	32	8-	M4(2).C2^3	128,1752
C₄².₁₃C₂³	13^rd non-split extension by C₄² of C₂³ acting faithfully	32	8-	C4^2.13C2^3	128,1754
C₂×C₂³.₇D₄	Direct product of C₂ and C₂³.₇D₄	32		C2xC2^3.7D4	128,1756
C₂³.₁₀C₂⁴	10^th non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	32	8-	C2^3.10C2^4	128,1760
C₄².₂₁₁D₄	193^rd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.211D4	128,1768
C₄².₄₄₄D₄	77^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	32		C4^2.444D4	128,1770
C₄².₄₄₆D₄	79^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	32		C4^2.446D4	128,1772
C₄².₁₄C₂³	14^th non-split extension by C₄² of C₂³ acting faithfully	32		C4^2.14C2^3	128,1773
C₄².₁₅C₂³	15^th non-split extension by C₄² of C₂³ acting faithfully	32		C4^2.15C2^3	128,1774
C₄².₁₆C₂³	16^th non-split extension by C₄² of C₂³ acting faithfully	32		C4^2.16C2^3	128,1775
C₄².₁₈C₂³	18^th non-split extension by C₄² of C₂³ acting faithfully	32		C4^2.18C2^3	128,1777
C₂⁴.₁₄₄D₄	13^rd non-split extension by C₂⁴ of D₄ acting via D₄/C₄=C₂	32		C2^4.144D4	128,1782
C₂⁴.₁₁₀D₄	65^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.110D4	128,1786
M₄(2)⋊₁₄D₄	1^st semidirect product of M₄(2) and D₄ acting via D₄/C₂²=C₂	32		M4(2):14D4	128,1787
M₄(2)⋊₁₅D₄	2^nd semidirect product of M₄(2) and D₄ acting via D₄/C₂²=C₂	32		M4(2):15D4	128,1788
(C₂×C₈)⋊₁₁D₄	7^th semidirect product of C₂×C₈ and D₄ acting via D₄/C₂=C₂²	32		(C2xC8):11D4	128,1789
(C₂×C₈)⋊₁₂D₄	8^th semidirect product of C₂×C₈ and D₄ acting via D₄/C₂=C₂²	32		(C2xC8):12D4	128,1790
M₄(2)⋊₁₆D₄	3^rd semidirect product of M₄(2) and D₄ acting via D₄/C₂²=C₂	32		M4(2):16D4	128,1794
C₂×D₄.₃D₄	Direct product of C₂ and D₄.₃D₄	32		C2xD4.3D4	128,1796
C₂×D₄.₄D₄	Direct product of C₂ and D₄.₄D₄	32		C2xD4.4D4	128,1797
M₄(2).₁₀C₂³	10^th non-split extension by M₄(2) of C₂³ acting via C₂³/C₂=C₂²	32	4	M4(2).10C2^3	128,1799
M₄(2).₃₈D₄	2^nd non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	32	8-	M4(2).38D4	128,1801
C₄².₂₁₉D₄	201^st non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.219D4	128,1809
C₄².₂₀C₂³	20^th non-split extension by C₄² of C₂³ acting faithfully	32		C4^2.20C2^3	128,1813
C₂⁴.₁₁₅D₄	70^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.115D4	128,1823
C₂⁴.₁₈₃D₄	38^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂²=C₂	32		C2^4.183D4	128,1824
C₂⁴.₁₁₆D₄	71^st non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.116D4	128,1825
C₂⁴.₁₁₇D₄	72^nd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.117D4	128,1826
C₂⁴.₁₁₈D₄	73^rd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.118D4	128,1827
(C₂×D₄).₃₀₁D₄	54^th non-split extension by C₂×D₄ of D₄ acting via D₄/C₂²=C₂	32		(C2xD4).301D4	128,1828
C₄².₂₂₁D₄	203^rd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.221D4	128,1832
C₄².₂₂₂D₄	204^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.222D4	128,1833
C₄².₂₂₅D₄	207^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.225D4	128,1837
C₄².₂₂₇D₄	209^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.227D4	128,1841
C₄².₂₂₈D₄	210^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.228D4	128,1842
C₄².₂₃₂D₄	214^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.232D4	128,1846
C₄².₃₅₂C₂³	213^rd non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.352C2^3	128,1850
C₄².₃₅₆C₂³	217^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.356C2^3	128,1854
C₄².₃₅₇C₂³	218^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.357C2^3	128,1855
C₄².₃₆₆C₂³	227^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.366C2^3	128,1868
C₄².₂₄₀D₄	222^nd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.240D4	128,1870
C₄².₂₄₂D₄	224^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.242D4	128,1872
M₄(2)⋊₇D₄	1^st semidirect product of M₄(2) and D₄ acting via D₄/C₄=C₂	32		M4(2):7D4	128,1883
M₄(2)⋊₉D₄	3^rd semidirect product of M₄(2) and D₄ acting via D₄/C₄=C₂	32		M4(2):9D4	128,1885
M₄(2)⋊₁₀D₄	4^th semidirect product of M₄(2) and D₄ acting via D₄/C₄=C₂	32		M4(2):10D4	128,1886
M₄(2)⋊₁₁D₄	5^th semidirect product of M₄(2) and D₄ acting via D₄/C₄=C₂	32		M4(2):11D4	128,1887
C₂³⋊₃D₈	2^nd semidirect product of C₂³ and D₈ acting via D₈/C₄=C₂²	32		C2^3:3D8	128,1918
C₂³⋊₄SD₁₆	2^nd semidirect product of C₂³ and SD₁₆ acting via SD₁₆/C₄=C₂²	32		C2^3:4SD16	128,1919
C₂⁴.₁₂₁D₄	76^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.121D4	128,1920
C₂³⋊₃Q₁₆	2^nd semidirect product of C₂³ and Q₁₆ acting via Q₁₆/C₄=C₂²	32		C2^3:3Q16	128,1921
C₂⁴.₁₂₃D₄	78^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.123D4	128,1922
C₂⁴.₁₂₄D₄	79^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.124D4	128,1923
C₂⁴.₁₂₅D₄	80^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.125D4	128,1924
C₂⁴.₁₂₆D₄	81^st non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.126D4	128,1925
C₂⁴.₁₂₇D₄	82^nd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.127D4	128,1926
C₂⁴.₁₂₈D₄	83^rd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.128D4	128,1927
C₂⁴.₁₂₉D₄	84^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.129D4	128,1928
C₂⁴.₁₃₀D₄	85^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	32		C2^4.130D4	128,1929
C₄.2₊¹⁺⁴	13^rd non-split extension by C₄ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	32		C4.ES+(2,2)	128,1930
C₄.₁₄2₊¹⁺⁴	14^th non-split extension by C₄ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	32		C4.14ES+(2,2)	128,1931
C₄.₁₅2₊¹⁺⁴	15^th non-split extension by C₄ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	32		C4.15ES+(2,2)	128,1932
C₄².₂₆₃D₄	245^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.263D4	128,1937
C₄².₂₆₆D₄	248^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.266D4	128,1940
C₄².₂₆₉D₄	251^st non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.269D4	128,1943
C₄².₂₇₁D₄	253^rd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.271D4	128,1945
C₄².₂₇₃D₄	255^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.273D4	128,1947
C₄².₂₇₅D₄	257^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	32		C4^2.275D4	128,1949
C₄².₄₀₆C₂³	267^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.406C2^3	128,1952
C₄².₄₀₈C₂³	269^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.408C2^3	128,1954
C₄².₄₁₀C₂³	271^st non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.410C2^3	128,1956
D₈⋊₉D₄	3^rd semidirect product of D₈ and D₄ acting via D₄/C₂²=C₂	32		D8:9D4	128,1996
SD₁₆⋊D₄	1^st semidirect product of SD₁₆ and D₄ acting via D₄/C₂²=C₂	32		SD16:D4	128,1997
SD₁₆⋊₆D₄	2^nd semidirect product of SD₁₆ and D₄ acting via D₄/C₂²=C₂	32		SD16:6D4	128,1998
D₈⋊₁₀D₄	4^th semidirect product of D₈ and D₄ acting via D₄/C₂²=C₂	32		D8:10D4	128,1999
SD₁₆⋊₇D₄	3^rd semidirect product of SD₁₆ and D₄ acting via D₄/C₂²=C₂	32		SD16:7D4	128,2000
D₈⋊₄D₄	3^rd semidirect product of D₈ and D₄ acting via D₄/C₄=C₂	32		D8:4D4	128,2004
D₈⋊₅D₄	4^th semidirect product of D₈ and D₄ acting via D₄/C₄=C₂	32		D8:5D4	128,2005
SD₁₆⋊₁D₄	1^st semidirect product of SD₁₆ and D₄ acting via D₄/C₄=C₂	32		SD16:1D4	128,2006
SD₁₆⋊₂D₄	2^nd semidirect product of SD₁₆ and D₄ acting via D₄/C₄=C₂	32		SD16:2D4	128,2007
D₄×D₈	Direct product of D₄ and D₈	32		D4xD8	128,2011
D₈⋊₁₂D₄	1^st semidirect product of D₈ and D₄ acting through Inn(D₈)	32		D8:12D4	128,2012
D₄×SD₁₆	Direct product of D₄ and SD₁₆	32		D4xSD16	128,2013
SD₁₆⋊₁₀D₄	1^st semidirect product of SD₁₆ and D₄ acting through Inn(SD₁₆)	32		SD16:10D4	128,2014
D₈.₁₃D₄	5^th non-split extension by D₈ of D₄ acting via D₄/C₂²=C₂	32	8-	D8.13D4	128,2021
D₈○SD₁₆	Central product of D₈ and SD₁₆	32	4	D8oSD16	128,2022
D₈○Q₁₆	Central product of D₈ and Q₁₆	32	4-	D8oQ16	128,2025
D₄⋊₄D₈	1^st semidirect product of D₄ and D₈ acting through Inn(D₄)	32		D4:4D8	128,2026
D₄⋊₇SD₁₆	1^st semidirect product of D₄ and SD₁₆ acting through Inn(D₄)	32		D4:7SD16	128,2027
C₄².₄₆₁C₂³	322^nd non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.461C2^3	128,2028
C₄².₄₆₂C₂³	323^rd non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.462C2^3	128,2029
C₄².₄₁C₂³	41^st non-split extension by C₄² of C₂³ acting faithfully	32		C4^2.41C2^3	128,2038
C₄².₄₅C₂³	45^th non-split extension by C₄² of C₂³ acting faithfully	32		C4^2.45C2^3	128,2042
C₄².₄₆C₂³	46^th non-split extension by C₄² of C₂³ acting faithfully	32		C4^2.46C2^3	128,2043
C₄².₄₉C₂³	49^th non-split extension by C₄² of C₂³ acting faithfully	32		C4^2.49C2^3	128,2046
C₄².₅₃C₂³	53^rd non-split extension by C₄² of C₂³ acting faithfully	32		C4^2.53C2^3	128,2050
C₄².₅₄C₂³	54^th non-split extension by C₄² of C₂³ acting faithfully	32		C4^2.54C2^3	128,2051
C₄².₄₇₁C₂³	332^nd non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.471C2^3	128,2054
C₄².₄₇₂C₂³	333^rd non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.472C2^3	128,2055
C₄².₄₇₃C₂³	334^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.473C2^3	128,2056
C₄².₄₇₄C₂³	335^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32		C4^2.474C2^3	128,2057
Q₈○M₅(2)	Central product of Q₈ and M₅(2)	32	4	Q8oM5(2)	128,2139
C₂×C₁₆⋊C₂²	Direct product of C₂ and C₁₆⋊C₂²	32		C2xC16:C2^2	128,2144
D₁₆⋊C₂²	4^th semidirect product of D₁₆ and C₂² acting via C₂²/C₂=C₂	32	4	D16:C2^2	128,2146
D₄○D₁₆	Central product of D₄ and D₁₆	32	4+	D4oD16	128,2147
D₄○SD₃₂	Central product of D₄ and SD₃₂	32	4	D4oSD32	128,2148
C₂×C₂².₁₁C₂⁴	Direct product of C₂ and C₂².₁₁C₂⁴	32		C2xC2^2.11C2^4	128,2157
C₂².₁₄C₂⁵	10^th central extension by C₂² of C₂⁵	32		C2^2.14C2^5	128,2160
C₄×2₊¹⁺⁴	Direct product of C₄ and 2₊¹⁺⁴	32		C4xES+(2,2)	128,2161
C₂²×C₂²≀C₂	Direct product of C₂² and C₂²≀C₂	32		C2^2xC2^2wrC2	128,2163
C₂×C₂².₁₉C₂⁴	Direct product of C₂ and C₂².₁₉C₂⁴	32		C2xC2^2.19C2^4	128,2167
C₂².₃₃C₂⁵	14^th central stem extension by C₂² of C₂⁵	32		C2^2.33C2^5	128,2176
C₂×C₂³⋊₃D₄	Direct product of C₂ and C₂³⋊₃D₄	32		C2xC2^3:3D4	128,2177
C₂×C₂².₂₉C₂⁴	Direct product of C₂ and C₂².₂₉C₂⁴	32		C2xC2^2.29C2^4	128,2178
C₂².₃₈C₂⁵	19^th central stem extension by C₂² of C₂⁵	32		C2^2.38C2^5	128,2181
C₂×C₂².₃₂C₂⁴	Direct product of C₂ and C₂².₃₂C₂⁴	32		C2xC2^2.32C2^4	128,2182
C₂².₄₄C₂⁵	25^th central stem extension by C₂² of C₂⁵	32		C2^2.44C2^5	128,2187
C₂×C₂³⋊₂Q₈	Direct product of C₂ and C₂³⋊₂Q₈	32		C2xC2^3:2Q8	128,2188
C₂².₄₇C₂⁵	28^th central stem extension by C₂² of C₂⁵	32		C2^2.47C2^5	128,2190
C₂².₄₈C₂⁵	29^th central stem extension by C₂² of C₂⁵	32		C2^2.48C2^5	128,2191
C₂².₄₉C₂⁵	30^th central stem extension by C₂² of C₂⁵	32		C2^2.49C2^5	128,2192
C₂×D₄²	Direct product of C₂, D₄ and D₄	32		C2xD4^2	128,2194
C₂×D₄⋊₅D₄	Direct product of C₂ and D₄⋊₅D₄	32		C2xD4:5D4	128,2195
D₄×C₄○D₄	Direct product of D₄ and C₄○D₄	32		D4xC4oD4	128,2200
C₂×C₂².₄₅C₂⁴	Direct product of C₂ and C₂².₄₅C₂⁴	32		C2xC2^2.45C2^4	128,2201
C₂².₆₄C₂⁵	45^th central stem extension by C₂² of C₂⁵	32		C2^2.64C2^5	128,2207
C₂².₇₀C₂⁵	51^st central stem extension by C₂² of C₂⁵	32		C2^2.70C2^5	128,2213
C₂².₇₄C₂⁵	55^th central stem extension by C₂² of C₂⁵	32		C2^2.74C2^5	128,2217
C₂².₇₅C₂⁵	56^th central stem extension by C₂² of C₂⁵	32		C2^2.75C2^5	128,2218
C₂².₇₆C₂⁵	57^th central stem extension by C₂² of C₂⁵	32		C2^2.76C2^5	128,2219
C₂².₇₇C₂⁵	58^th central stem extension by C₂² of C₂⁵	32		C2^2.77C2^5	128,2220
C₂².₇₈C₂⁵	59^th central stem extension by C₂² of C₂⁵	32		C2^2.78C2^5	128,2221
C₂².₈₀C₂⁵	61^st central stem extension by C₂² of C₂⁵	32		C2^2.80C2^5	128,2223
C₂².₈₁C₂⁵	62^nd central stem extension by C₂² of C₂⁵	32		C2^2.81C2^5	128,2224
C₂².₈₂C₂⁵	63^rd central stem extension by C₂² of C₂⁵	32		C2^2.82C2^5	128,2225
C₂².₈₃C₂⁵	64^th central stem extension by C₂² of C₂⁵	32		C2^2.83C2^5	128,2226
C₂².₈₄C₂⁵	65^th central stem extension by C₂² of C₂⁵	32		C2^2.84C2^5	128,2227
C₄⋊2₊¹⁺⁴	The semidirect product of C₄ and 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	32		C4:ES+(2,2)	128,2228
C₂².₈₇C₂⁵	68^th central stem extension by C₂² of C₂⁵	32		C2^2.87C2^5	128,2230
C₂².₈₉C₂⁵	70^th central stem extension by C₂² of C₂⁵	32		C2^2.89C2^5	128,2232
C₂².₉₀C₂⁵	71^st central stem extension by C₂² of C₂⁵	32		C2^2.90C2^5	128,2233
C₂².₉₄C₂⁵	75^th central stem extension by C₂² of C₂⁵	32		C2^2.94C2^5	128,2237
C₂².₉₅C₂⁵	76^th central stem extension by C₂² of C₂⁵	32		C2^2.95C2^5	128,2238
C₂².₉₇C₂⁵	78^th central stem extension by C₂² of C₂⁵	32		C2^2.97C2^5	128,2240
C₂².₉₉C₂⁵	80^th central stem extension by C₂² of C₂⁵	32		C2^2.99C2^5	128,2242
C₂².₁₀₂C₂⁵	83^rd central stem extension by C₂² of C₂⁵	32		C2^2.102C2^5	128,2245
C₂².₁₀₃C₂⁵	84^th central stem extension by C₂² of C₂⁵	32		C2^2.103C2^5	128,2246
C₂².₁₀₈C₂⁵	89^th central stem extension by C₂² of C₂⁵	32		C2^2.108C2^5	128,2251
C₂³.₁₄₄C₂⁴	44^th non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂³=C₂	32		C2^3.144C2^4	128,2252
C₂².₁₁₀C₂⁵	91^st central stem extension by C₂² of C₂⁵	32		C2^2.110C2^5	128,2253
C₂×C₂².₅₄C₂⁴	Direct product of C₂ and C₂².₅₄C₂⁴	32		C2xC2^2.54C2^4	128,2257
C₂×C₂⁴⋊C₂²	Direct product of C₂ and C₂⁴⋊C₂²	32		C2xC2^4:C2^2	128,2258
C₂².₁₁₈C₂⁵	99^th central stem extension by C₂² of C₂⁵	32		C2^2.118C2^5	128,2261
C₂².₁₂₂C₂⁵	103^rd central stem extension by C₂² of C₂⁵	32		C2^2.122C2^5	128,2265
C₂².₁₂₃C₂⁵	104^th central stem extension by C₂² of C₂⁵	32		C2^2.123C2^5	128,2266
C₂².₁₂₄C₂⁵	105^th central stem extension by C₂² of C₂⁵	32		C2^2.124C2^5	128,2267
C₂².₁₂₅C₂⁵	106^th central stem extension by C₂² of C₂⁵	32		C2^2.125C2^5	128,2268
C₂².₁₂₆C₂⁵	107^th central stem extension by C₂² of C₂⁵	32		C2^2.126C2^5	128,2269
C₂².₁₂₇C₂⁵	108^th central stem extension by C₂² of C₂⁵	32		C2^2.127C2^5	128,2270
C₂².₁₂₈C₂⁵	109^th central stem extension by C₂² of C₂⁵	32		C2^2.128C2^5	128,2271
C₂².₁₂₉C₂⁵	110^th central stem extension by C₂² of C₂⁵	32		C2^2.129C2^5	128,2272
C₂².₁₃₀C₂⁵	111^st central stem extension by C₂² of C₂⁵	32		C2^2.130C2^5	128,2273
C₂².₁₃₁C₂⁵	112^nd central stem extension by C₂² of C₂⁵	32		C2^2.131C2^5	128,2274
C₂².₁₃₂C₂⁵	113^rd central stem extension by C₂² of C₂⁵	32		C2^2.132C2^5	128,2275
C₂².₁₃₄C₂⁵	115^th central stem extension by C₂² of C₂⁵	32		C2^2.134C2^5	128,2277
C₂².₁₃₅C₂⁵	116^th central stem extension by C₂² of C₂⁵	32		C2^2.135C2^5	128,2278
C₂².₁₃₈C₂⁵	119^th central stem extension by C₂² of C₂⁵	32		C2^2.138C2^5	128,2281
C₂².₁₄₀C₂⁵	121^st central stem extension by C₂² of C₂⁵	32		C2^2.140C2^5	128,2283
C₂².₁₄₇C₂⁵	128^th central stem extension by C₂² of C₂⁵	32		C2^2.147C2^5	128,2290
C₂².₁₄₉C₂⁵	130^th central stem extension by C₂² of C₂⁵	32		C2^2.149C2^5	128,2292
C₂².₁₅₀C₂⁵	131^st central stem extension by C₂² of C₂⁵	32		C2^2.150C2^5	128,2293
C₂².₁₅₁C₂⁵	132^nd central stem extension by C₂² of C₂⁵	32		C2^2.151C2^5	128,2294
C₂².₁₅₃C₂⁵	134^th central stem extension by C₂² of C₂⁵	32		C2^2.153C2^5	128,2296
C₂².₁₅₅C₂⁵	136^th central stem extension by C₂² of C₂⁵	32		C2^2.155C2^5	128,2298
C₂².₁₅₇C₂⁵	138^th central stem extension by C₂² of C₂⁵	32		C2^2.157C2^5	128,2300
C₂×Q₈○M₄(2)	Direct product of C₂ and Q₈○M₄(2)	32		C2xQ8oM4(2)	128,2304
C₄.₂₂C₂⁵	4^th central extension by C₄ of C₂⁵	32	4	C4.22C2^5	128,2305
C₂²×C₈⋊C₂²	Direct product of C₂² and C₈⋊C₂²	32		C2^2xC8:C2^2	128,2310
C₂×D₈⋊C₂²	Direct product of C₂ and D₈⋊C₂²	32		C2xD8:C2^2	128,2312
C₂×D₄○D₈	Direct product of C₂ and D₄○D₈	32		C2xD4oD8	128,2313
C₂×D₄○SD₁₆	Direct product of C₂ and D₄○SD₁₆	32		C2xD4oSD16	128,2314
C₈.C₂⁴	6^th non-split extension by C₈ of C₂⁴ acting via C₂⁴/C₂²=C₂²	32	4	C8.C2^4	128,2316
C₄.C₂⁵	13^rd non-split extension by C₄ of C₂⁵ acting via C₂⁵/C₂⁴=C₂	32	8-	C4.C2^5	128,2318
C₂²×2₊¹⁺⁴	Direct product of C₂² and 2₊¹⁺⁴	32		C2^2xES+(2,2)	128,2323
C₂×C₂.C₂⁵	Direct product of C₂ and C₂.C₂⁵	32		C2xC2.C2^5	128,2325
2_-¹⁺⁶	Extraspecial group; = D₄ ○2_-¹⁺⁴	32	8-	ES-(2,3)	128,2327

Groups of order 160

		d	ρ	Label	ID
2_-¹⁺⁴⋊C₅	The semidirect product of 2_-¹⁺⁴ and C₅ acting faithfully	32	4-	ES-(2,2):C5	160,199

Groups of order 192

		d	ρ	Label	ID
C₄×GL₂(𝔽₃)	Direct product of C₄ and GL₂(𝔽₃)	32		C4xGL(2,3)	192,951
Q₈⋊D₁₂	The semidirect product of Q₈ and D₁₂ acting via D₁₂/C₄=S₃	32		Q8:D12	192,952
GL₂(𝔽₃)⋊C₄	1^st semidirect product of GL₂(𝔽₃) and C₄ acting via C₄/C₂=C₂	32		GL(2,3):C4	192,953
Q₈.₂D₁₂	2^nd non-split extension by Q₈ of D₁₂ acting via D₁₂/C₄=S₃	32		Q8.2D12	192,954
CU₂(𝔽₃)	Conformal unitary group on 𝔽₃²; = U₂(𝔽₃)⋊₇ C₂	32	2	CU(2,3)	192,963
C₈.₅S₄	5^th non-split extension by C₈ of S₄ acting via S₄/A₄=C₂	32	4	C8.5S4	192,964
C₈.₄S₄	4^th non-split extension by C₈ of S₄ acting via S₄/A₄=C₂	32	4	C8.4S4	192,965
C₈.₃S₄	3^rd non-split extension by C₈ of S₄ acting via S₄/A₄=C₂	32	4+	C8.3S4	192,966
C₂³.₁₄S₄	1^st non-split extension by C₂³ of S₄ acting via S₄/A₄=C₂	32		C2^3.14S4	192,978
C₂³.₁₅S₄	2^nd non-split extension by C₂³ of S₄ acting via S₄/A₄=C₂	32		C2^3.15S4	192,979
C₂³.₁₆S₄	3^rd non-split extension by C₂³ of S₄ acting via S₄/A₄=C₂	32		C2^3.16S4	192,980
U₂(𝔽₃)⋊C₂	6^th semidirect product of U₂(𝔽₃) and C₂ acting faithfully	32	4	U(2,3):C2	192,982
SL₂(𝔽₃)⋊D₄	2^nd semidirect product of SL₂(𝔽₃) and D₄ acting via D₄/C₂²=C₂	32		SL(2,3):D4	192,986
D₄.S₄	2^nd non-split extension by D₄ of S₄ acting via S₄/A₄=C₂	32	4-	D4.S4	192,989
D₄.₃S₄	3^rd non-split extension by D₄ of S₄ acting via S₄/A₄=C₂	32	4	D4.3S4	192,990
(C₂×Q₈)⋊C₁₂	The semidirect product of C₂×Q₈ and C₁₂ acting via C₁₂/C₂=C₆	32		(C2xQ8):C12	192,998
SL₂(𝔽₃)⋊₅D₄	1^st semidirect product of SL₂(𝔽₃) and D₄ acting through Inn(SL₂(𝔽₃))	32		SL(2,3):5D4	192,1003
D₄×SL₂(𝔽₃)	Direct product of D₄ and SL₂(𝔽₃)	32		D4xSL(2,3)	192,1004
M₄(2).A₄	The non-split extension by M₄(2) of A₄ acting through Inn(M₄(2))	32	4	M4(2).A4	192,1013
SD₁₆.A₄	The non-split extension by SD₁₆ of A₄ acting through Inn(SD₁₆)	32	4	SD16.A4	192,1018
D₈.A₄	The non-split extension by D₈ of A₄ acting through Inn(D₈)	32	4-	D8.A4	192,1019
C₂²×GL₂(𝔽₃)	Direct product of C₂² and GL₂(𝔽₃)	32		C2^2xGL(2,3)	192,1475
C₂×Q₈.D₆	Direct product of C₂ and Q₈.D₆	32		C2xQ8.D6	192,1476
C₂×C₄.₆S₄	Direct product of C₂ and C₄.₆S₄	32		C2xC4.6S4	192,1480
C₂×C₄.₃S₄	Direct product of C₂ and C₄.₃S₄	32		C2xC4.3S4	192,1481
GL₂(𝔽₃)⋊C₂²	3^rd semidirect product of GL₂(𝔽₃) and C₂² acting via C₂²/C₂=C₂	32	4	GL(2,3):C2^2	192,1482
Q₈.₆S₄	1^st non-split extension by Q₈ of S₄ acting through Inn(Q₈)	32	4	Q8.6S4	192,1483
Q₈.₇S₄	2^nd non-split extension by Q₈ of S₄ acting through Inn(Q₈)	32	4+	Q8.7S4	192,1484
D₄.₅S₄	2^nd non-split extension by D₄ of S₄ acting through Inn(D₄)	32	4-	D4.5S4	192,1486
C₂×D₄.A₄	Direct product of C₂ and D₄.A₄	32		C2xD4.A4	192,1503
2_-¹⁺⁴⋊₃C₆	2^nd semidirect product of 2_-¹⁺⁴ and C₆ acting via C₆/C₂=C₃	32	4	ES-(2,2):3C6	192,1504

Groups of order 320

		d	ρ	Label	ID
2_-¹⁺⁴⋊D₅	The semidirect product of 2_-¹⁺⁴ and D₅ acting faithfully	32	4	ES-(2,2):D5	320,1582

On 33 points

Groups of order 33

		d	ρ	Label	ID
C₃₃	Cyclic group	33	1	C33	33,1

Groups of order 66

		d	ρ	Label	ID
S₃×C₁₁	Direct product of C₁₁ and S₃	33	2	S3xC11	66,1
C₃×D₁₁	Direct product of C₃ and D₁₁	33	2	C3xD11	66,2
D₃₃	Dihedral group	33	2+	D33	66,3

Groups of order 132

		d	ρ	Label	ID
S₃×D₁₁	Direct product of S₃ and D₁₁	33	4+	S3xD11	132,5

Groups of order 165

		d	ρ	Label	ID
C₃×C₁₁⋊C₅	Direct product of C₃ and C₁₁⋊C₅	33	5	C3xC11:C5	165,1

Groups of order 330

		d	ρ	Label	ID
C₃×F₁₁	Direct product of C₃ and F₁₁	33	10	C3xF11	330,1
S₃×C₁₁⋊C₅	Direct product of S₃ and C₁₁⋊C₅	33	10	S3xC11:C5	330,2
C₃⋊F₁₁	The semidirect product of C₃ and F₁₁ acting via F₁₁/C₁₁⋊C₅=C₂	33	10+	C3:F11	330,3

Groups of order 363

		d	ρ	Label	ID
C₁₁²⋊C₃	The semidirect product of C₁₁² and C₃ acting faithfully	33	3	C11^2:C3	363,2

On 34 points

Groups of order 34

		d	ρ	Label	ID
C₃₄	Cyclic group	34	1	C34	34,2

Groups of order 68

		d	ρ	Label	ID
D₃₄	Dihedral group; = C₂×D₁₇	34	2+	D34	68,4

Groups of order 136

		d	ρ	Label	ID
C₂×C₁₇⋊C₄	Direct product of C₂ and C₁₇⋊C₄	34	4+	C2xC17:C4	136,13

Groups of order 272

		d	ρ	Label	ID
C₂×C₁₇⋊C₈	Direct product of C₂ and C₁₇⋊C₈	34	8+	C2xC17:C8	272,51

On 35 points

Groups of order 35

		d	ρ	Label	ID
C₃₅	Cyclic group	35	1	C35	35,1

Groups of order 70

		d	ρ	Label	ID
C₇×D₅	Direct product of C₇ and D₅	35	2	C7xD5	70,1
C₅×D₇	Direct product of C₅ and D₇	35	2	C5xD7	70,2
D₃₅	Dihedral group	35	2+	D35	70,3

Groups of order 105

		d	ρ	Label	ID
C₅×C₇⋊C₃	Direct product of C₅ and C₇⋊C₃	35	3	C5xC7:C3	105,1

Groups of order 140

		d	ρ	Label	ID
C₇×F₅	Direct product of C₇ and F₅	35	4	C7xF5	140,5
C₇⋊F₅	The semidirect product of C₇ and F₅ acting via F₅/D₅=C₂	35	4	C7:F5	140,6
D₅×D₇	Direct product of D₅ and D₇	35	4+	D5xD7	140,7

Groups of order 210

		d	ρ	Label	ID
C₅×F₇	Direct product of C₅ and F₇	35	6	C5xF7	210,1
D₅×C₇⋊C₃	Direct product of D₅ and C₇⋊C₃	35	6	D5xC7:C3	210,2
C₅⋊F₇	The semidirect product of C₅ and F₇ acting via F₇/C₇⋊C₃=C₂	35	6+	C5:F7	210,3

Groups of order 280

		d	ρ	Label	ID
D₇×F₅	Direct product of D₇ and F₅	35	8+	D7xF5	280,32

Groups of order 420

		d	ρ	Label	ID
C₇×A₅	Direct product of C₇ and A₅	35	3	C7xA5	420,13
F₅×C₇⋊C₃	Direct product of F₅ and C₇⋊C₃	35	12	F5xC7:C3	420,14
C₃₅⋊C₁₂	1^st semidirect product of C₃₅ and C₁₂ acting faithfully	35	12	C35:C12	420,15
D₅×F₇	Direct product of D₅ and F₇	35	12+	D5xF7	420,16

On 36 points

Groups of order 36

		d	ρ	Label	ID
Dic₉	Dicyclic group; = C₉ ⋊C₄	36	2-	Dic9	36,1
C₃₆	Cyclic group	36	1	C36	36,2
C₂×C₁₈	Abelian group of type [2,18]	36		C2xC18	36,5
C₃⋊Dic₃	The semidirect product of C₃ and Dic₃ acting via Dic₃/C₆=C₂	36		C3:Dic3	36,7
C₃×C₁₂	Abelian group of type [3,12]	36		C3xC12	36,8
C₆²	Abelian group of type [6,6]	36		C6^2	36,14

Groups of order 72

		d	ρ	Label	ID
C₄×D₉	Direct product of C₄ and D₉	36	2	C4xD9	72,5
D₃₆	Dihedral group	36	2+	D36	72,6
C₉⋊D₄	The semidirect product of C₉ and D₄ acting via D₄/C₂²=C₂	36	2	C9:D4	72,8
D₄×C₉	Direct product of C₉ and D₄	36	2	D4xC9	72,10
C₂²×D₉	Direct product of C₂² and D₉	36		C2^2xD9	72,17
C₄×C₃⋊S₃	Direct product of C₄ and C₃⋊S₃	36		C4xC3:S3	72,32
C₁₂⋊S₃	1^st semidirect product of C₁₂ and S₃ acting via S₃/C₃=C₂	36		C12:S3	72,33
C₃²⋊₇D₄	2^nd semidirect product of C₃² and D₄ acting via D₄/C₂²=C₂	36		C3^2:7D4	72,35
D₄×C₃²	Direct product of C₃² and D₄	36		D4xC3^2	72,37
C₂²×C₃⋊S₃	Direct product of C₂² and C₃⋊S₃	36		C2^2xC3:S3	72,49

Groups of order 108

		d	ρ	Label	ID
C₃×Dic₉	Direct product of C₃ and Dic₉	36	2	C3xDic9	108,6
C₉×Dic₃	Direct product of C₉ and Dic₃	36	2	C9xDic3	108,7
C₃²⋊C₁₂	The semidirect product of C₃² and C₁₂ acting via C₁₂/C₂=C₆	36	6-	C3^2:C12	108,8
C₉⋊C₁₂	The semidirect product of C₉ and C₁₂ acting via C₁₂/C₂=C₆	36	6-	C9:C12	108,9
He₃⋊₃C₄	2^nd semidirect product of He₃ and C₄ acting via C₄/C₂=C₂	36	3	He3:3C4	108,11
C₄×He₃	Direct product of C₄ and He₃	36	3	C4xHe3	108,13
C₄×3_-¹⁺²	Direct product of C₄ and 3_-¹⁺²	36	3	C4xES-(3,1)	108,14
C₉×A₄	Direct product of C₉ and A₄	36	3	C9xA4	108,18
C₉⋊A₄	The semidirect product of C₉ and A₄ acting via A₄/C₂²=C₃	36	3	C9:A4	108,19
C₆×D₉	Direct product of C₆ and D₉	36	2	C6xD9	108,23
S₃×C₁₈	Direct product of C₁₈ and S₃	36	2	S3xC18	108,24
C₂²×He₃	Direct product of C₂² and He₃	36		C2^2xHe3	108,30
C₂²×3_-¹⁺²	Direct product of C₂² and 3_-¹⁺²	36		C2^2xES-(3,1)	108,31
C₃²×Dic₃	Direct product of C₃² and Dic₃	36		C3^2xDic3	108,32
C₃×C₃⋊Dic₃	Direct product of C₃ and C₃⋊Dic₃	36		C3xC3:Dic3	108,33
C₃²×A₄	Direct product of C₃² and A₄	36		C3^2xA4	108,41
S₃×C₃×C₆	Direct product of C₃×C₆ and S₃	36		S3xC3xC6	108,42
C₆×C₃⋊S₃	Direct product of C₆ and C₃⋊S₃	36		C6xC3:S3	108,43

Groups of order 144

		d	ρ	Label	ID
C₄²⋊C₉	The semidirect product of C₄² and C₉ acting via C₉/C₃=C₃	36	3	C4^2:C9	144,3
C₆.S₄	3^rd non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	36	6-	C6.S4	144,33
C₄×C₃.A₄	Direct product of C₄ and C₃.A₄	36	3	C4xC3.A4	144,34
D₄×D₉	Direct product of D₄ and D₉	36	4+	D4xD9	144,41
C₃×C₄²⋊C₃	Direct product of C₃ and C₄²⋊C₃	36	3	C3xC4^2:C3	144,68
C₂²×C₃.A₄	Direct product of C₂² and C₃.A₄	36		C2^2xC3.A4	144,110
C₂⁴⋊C₉	2^nd semidirect product of C₂⁴ and C₉ acting via C₉/C₃=C₃	36		C2^4:C9	144,111
C₃×A₄⋊C₄	Direct product of C₃ and A₄⋊C₄	36	3	C3xA4:C4	144,123
C₆.₇S₄	7^th non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	36	6-	C6.7S4	144,126
Dic₃×A₄	Direct product of Dic₃ and A₄	36	6-	Dic3xA4	144,129
C₁₂×A₄	Direct product of C₁₂ and A₄	36	3	C12xA4	144,155
D₄×C₃⋊S₃	Direct product of D₄ and C₃⋊S₃	36		D4xC3:S3	144,172
A₄×C₂×C₆	Direct product of C₂×C₆ and A₄	36		A4xC2xC6	144,193
C₃×C₂²⋊A₄	Direct product of C₃ and C₂²⋊A₄	36		C3xC2^2:A4	144,194

Groups of order 216

		d	ρ	Label	ID
C₁₈.D₆	3^rd non-split extension by C₁₈ of D₆ acting via D₆/S₃=C₂	36	4+	C18.D6	216,28
C₃⋊D₃₆	The semidirect product of C₃ and D₃₆ acting via D₃₆/D₁₈=C₂	36	4+	C3:D36	216,29
C₉⋊D₁₂	The semidirect product of C₉ and D₁₂ acting via D₁₂/D₆=C₂	36	4+	C9:D12	216,32
C₆.S₃²	2^nd non-split extension by C₆ of S₃² acting via S₃²/C₃⋊S₃=C₂	36	6	C6.S3^2	216,34
He₃⋊₂D₄	1^st semidirect product of He₃ and D₄ acting via D₄/C₂=C₂²	36	6+	He3:2D4	216,35
He₃⋊(C₂×C₄)	2^nd semidirect product of He₃ and C₂×C₄ acting via C₂×C₄/C₂=C₂²	36	6-	He3:(C2xC4)	216,36
He₃⋊₃D₄	2^nd semidirect product of He₃ and D₄ acting via D₄/C₂=C₂²	36	6	He3:3D4	216,37
C₄×C₃²⋊C₆	Direct product of C₄ and C₃²⋊C₆	36	6	C4xC3^2:C6	216,50
He₃⋊₄D₄	1^st semidirect product of He₃ and D₄ acting via D₄/C₄=C₂	36	6+	He3:4D4	216,51
C₄×C₉⋊C₆	Direct product of C₄ and C₉⋊C₆	36	6	C4xC9:C6	216,53
D₃₆⋊C₃	The semidirect product of D₃₆ and C₃ acting faithfully	36	6+	D36:C3	216,54
C₃×C₉⋊D₄	Direct product of C₃ and C₉⋊D₄	36	2	C3xC9:D4	216,57
C₉×C₃⋊D₄	Direct product of C₉ and C₃⋊D₄	36	2	C9xC3:D4	216,58
He₃⋊₆D₄	1^st semidirect product of He₃ and D₄ acting via D₄/C₂²=C₂	36	6	He3:6D4	216,60
Dic₉⋊C₆	The semidirect product of Dic₉ and C₆ acting faithfully	36	6	Dic9:C6	216,62
C₄×He₃⋊C₂	Direct product of C₄ and He₃⋊C₂	36	3	C4xHe3:C2	216,67
He₃⋊₅D₄	2^nd semidirect product of He₃ and D₄ acting via D₄/C₄=C₂	36	6	He3:5D4	216,68
He₃⋊₇D₄	2^nd semidirect product of He₃ and D₄ acting via D₄/C₂²=C₂	36	6	He3:7D4	216,72
D₄×He₃	Direct product of D₄ and He₃	36	6	D4xHe3	216,77
D₄×3_-¹⁺²	Direct product of D₄ and 3_-¹⁺²	36	6	D4xES-(3,1)	216,78
C₉×S₄	Direct product of C₉ and S₄	36	3	C9xS4	216,89
C₃×C₃.S₄	Direct product of C₃ and C₃.S₄	36	6	C3xC3.S4	216,91
C₉⋊S₄	The semidirect product of C₉ and S₄ acting via S₄/A₄=C₂	36	6+	C9:S4	216,93
D₉⋊A₄	The semidirect product of D₉ and A₄ acting via A₄/C₂²=C₃	36	6+	D9:A4	216,96
A₄×D₉	Direct product of A₄ and D₉	36	6+	A4xD9	216,97
S₃×C₃.A₄	Direct product of S₃ and C₃.A₄	36	6	S3xC3.A4	216,98
C₂×He₃⋊C₄	Direct product of C₂ and He₃⋊C₄	36	3	C2xHe3:C4	216,100
C₂×S₃×D₉	Direct product of C₂, S₃ and D₉	36	4+	C2xS3xD9	216,101
C₂²×C₃²⋊C₆	Direct product of C₂² and C₃²⋊C₆	36		C2^2xC3^2:C6	216,110
C₂²×C₉⋊C₆	Direct product of C₂² and C₉⋊C₆	36		C2^2xC9:C6	216,111
C₂²×He₃⋊C₂	Direct product of C₂² and He₃⋊C₂	36		C2^2xHe3:C2	216,113
C₃³⋊₈(C₂×C₄)	5^th semidirect product of C₃³ and C₂×C₄ acting via C₂×C₄/C₂=C₂²	36		C3^3:8(C2xC4)	216,126
C₃³⋊₇D₄	4^th semidirect product of C₃³ and D₄ acting via D₄/C₂=C₂²	36		C3^3:7D4	216,128
C₃³⋊₈D₄	5^th semidirect product of C₃³ and D₄ acting via D₄/C₂=C₂²	36		C3^3:8D4	216,129
C₃²×C₃⋊D₄	Direct product of C₃² and C₃⋊D₄	36		C3^2xC3:D4	216,139
C₃×C₃²⋊₇D₄	Direct product of C₃ and C₃²⋊₇D₄	36		C3xC3^2:7D4	216,144
C₃²×S₄	Direct product of C₃² and S₄	36		C3^2xS4	216,163
C₃²⋊₄S₄	2^nd semidirect product of C₃² and S₄ acting via S₄/A₄=C₂	36		C3^2:4S4	216,165
A₄×C₃⋊S₃	Direct product of A₄ and C₃⋊S₃	36		A4xC3:S3	216,167
C₂×S₃×C₃⋊S₃	Direct product of C₂, S₃ and C₃⋊S₃	36		C2xS3xC3:S3	216,171

Groups of order 288

		d	ρ	Label	ID
C₂.(C₄²⋊C₉)	The central stem extension by C₂ of C₄²⋊C₉	36	6	C2.(C4^2:C9)	288,3
C₄²⋊D₉	The semidirect product of C₄² and D₉ acting via D₉/C₃=S₃	36	6+	C4^2:D9	288,67
C₂×C₄²⋊C₉	Direct product of C₂ and C₄²⋊C₉	36	3	C2xC4^2:C9	288,71
C₂⁴⋊C₁₈	1^st semidirect product of C₂⁴ and C₁₈ acting via C₁₈/C₃=C₆	36	6	C2^4:C18	288,73
C₄²⋊₂C₁₈	2^nd semidirect product of C₄² and C₁₈ acting via C₁₈/C₃=C₆	36	6	C4^2:2C18	288,75
C₃×C₂³.₃A₄	Direct product of C₃ and C₂³.₃A₄	36	6	C3xC2^3.3A4	288,230
C₄×C₃.S₄	Direct product of C₄ and C₃.S₄	36	6	C4xC3.S4	288,333
C₂²⋊D₃₆	The semidirect product of C₂² and D₃₆ acting via D₃₆/C₁₂=S₃	36	6+	C2^2:D36	288,334
C₂³.D₁₈	5^th non-split extension by C₂³ of D₁₈ acting via D₁₈/C₆=S₃	36	6	C2^3.D18	288,342
D₄×C₃.A₄	Direct product of D₄ and C₃.A₄	36	6	D4xC3.A4	288,344
C₃×C₄²⋊S₃	Direct product of C₃ and C₄²⋊S₃	36	3	C3xC4^2:S3	288,397
(C₄×C₁₂)⋊S₃	1^st semidirect product of C₄×C₁₂ and S₃ acting faithfully	36	6+	(C4xC12):S3	288,401
(C₄×C₁₂)⋊C₆	3^rd semidirect product of C₄×C₁₂ and C₆ acting faithfully	36	6+	(C4xC12):C6	288,405
S₃×C₄²⋊C₃	Direct product of S₃ and C₄²⋊C₃	36	6	S3xC4^2:C3	288,407
C₆×C₄²⋊C₃	Direct product of C₆ and C₄²⋊C₃	36	3	C6xC4^2:C3	288,632
C₃×C₂³.A₄	Direct product of C₃ and C₂³.A₄	36	6	C3xC2^3.A4	288,636
C₂²×C₃.S₄	Direct product of C₂² and C₃.S₄	36		C2^2xC3.S4	288,835
C₂⁴⋊D₉	3^rd semidirect product of C₂⁴ and D₉ acting via D₉/C₃=S₃	36	6	C2^4:D9	288,836
C₂×C₂⁴⋊C₉	Direct product of C₂ and C₂⁴⋊C₉	36		C2xC2^4:C9	288,838
PSU₃(𝔽₂)⋊C₄	The semidirect product of PSU₃(𝔽₂) and C₄ acting via C₄/C₂=C₂	36	8	PSU(3,2):C4	288,842
F₉⋊C₄	The semidirect product of F₉ and C₄ acting via C₄/C₂=C₂	36	8	F9:C4	288,843
Dic₃×S₄	Direct product of Dic₃ and S₄	36	6-	Dic3xS4	288,853
Dic₃⋊₂S₄	The semidirect product of Dic₃ and S₄ acting through Inn(Dic₃)	36	6	Dic3:2S4	288,854
Dic₃⋊S₄	The semidirect product of Dic₃ and S₄ acting via S₄/A₄=C₂	36	6	Dic3:S4	288,855
S₃×A₄⋊C₄	Direct product of S₃ and A₄⋊C₄	36	6	S3xA4:C4	288,856
D₆⋊S₄	1^st semidirect product of D₆ and S₄ acting via S₄/A₄=C₂	36	6	D6:S4	288,857
A₄⋊D₁₂	The semidirect product of A₄ and D₁₂ acting via D₁₂/D₆=C₂	36	6+	A4:D12	288,858
C₄×F₉	Direct product of C₄ and F₉	36	8	C4xF9	288,863
C₄⋊F₉	The semidirect product of C₄ and F₉ acting via F₉/C₃²⋊C₄=C₂	36	8	C4:F9	288,864
C₄×PSU₃(𝔽₂)	Direct product of C₄ and PSU₃(𝔽₂)	36	8	C4xPSU(3,2)	288,892
C₄⋊PSU₃(𝔽₂)	The semidirect product of C₄ and PSU₃(𝔽₂) acting via PSU₃(𝔽₂)/C₃²⋊C₄=C₂	36	8	C4:PSU(3,2)	288,893
C₁₂×S₄	Direct product of C₁₂ and S₄	36	3	C12xS4	288,897
C₃×C₄⋊S₄	Direct product of C₃ and C₄⋊S₄	36	6	C3xC4:S4	288,898
C₃×A₄⋊D₄	Direct product of C₃ and A₄⋊D₄	36	6	C3xA4:D4	288,906
C₄×C₃⋊S₄	Direct product of C₄ and C₃⋊S₄	36	6	C4xC3:S4	288,908
C₁₂⋊S₄	1^st semidirect product of C₁₂ and S₄ acting via S₄/A₄=C₂	36	6+	C12:S4	288,909
(C₂×C₆)⋊₄S₄	2^nd semidirect product of C₂×C₆ and S₄ acting via S₄/A₄=C₂	36	6	(C2xC6):4S4	288,917
C₄×S₃×A₄	Direct product of C₄, S₃ and A₄	36	6	C4xS3xA4	288,919
A₄×D₁₂	Direct product of A₄ and D₁₂	36	6+	A4xD12	288,920
A₄×C₃⋊D₄	Direct product of A₄ and C₃⋊D₄	36	6	A4xC3:D4	288,928
C₃×D₄×A₄	Direct product of C₃, D₄ and A₄	36	6	C3xD4xA4	288,980
C₂²×F₉	Direct product of C₂² and F₉	36		C2^2xF9	288,1030
C₂²×PSU₃(𝔽₂)	Direct product of C₂² and PSU₃(𝔽₂)	36		C2^2xPSU(3,2)	288,1032
C₂×C₆×S₄	Direct product of C₂×C₆ and S₄	36		C2xC6xS4	288,1033
C₂²×C₃⋊S₄	Direct product of C₂² and C₃⋊S₄	36		C2^2xC3:S4	288,1034
C₂²×S₃×A₄	Direct product of C₂², S₃ and A₄	36		C2^2xS3xA4	288,1037
S₃×C₂²⋊A₄	Direct product of S₃ and C₂²⋊A₄	36		S3xC2^2:A4	288,1038
C₆×C₂²⋊A₄	Direct product of C₆ and C₂²⋊A₄	36		C6xC2^2:A4	288,1042

Groups of order 324

		d	ρ	Label	ID
C₉×Dic₉	Direct product of C₉ and Dic₉	36	2	C9xDic9	324,6
C₃²⋊C₃₆	The semidirect product of C₃² and C₃₆ acting via C₃₆/C₆=C₆	36	6	C3^2:C36	324,7
C₉⋊C₃₆	The semidirect product of C₉ and C₃₆ acting via C₃₆/C₆=C₆	36	6	C9:C36	324,9
He₃⋊C₁₂	The semidirect product of He₃ and C₁₂ acting via C₁₂/C₂=C₆	36	3	He3:C12	324,13
C₃³⋊C₁₂	1^st semidirect product of C₃³ and C₁₂ acting via C₁₂/C₂=C₆	36	6-	C3^3:C12	324,14
C₃²⋊₂Dic₉	2^nd semidirect product of C₃² and Dic₉ acting via Dic₉/C₆=S₃	36	6	C3^2:2Dic9	324,20
C₃³⋊Dic₃	2^nd semidirect product of C₃³ and Dic₃ acting via Dic₃/C₂=S₃	36	6-	C3^3:Dic3	324,22
C₄×C₃≀C₃	Direct product of C₄ and C₃≀C₃	36	3	C4xC3wrC3	324,31
He₃⋊₂A₄	2^nd semidirect product of He₃ and A₄ acting via A₄/C₂²=C₃	36	9	He3:2A4	324,55
C₆².₆C₃²	6^th non-split extension by C₆² of C₃² acting faithfully	36	9	C6^2.6C3^2	324,58
D₉×C₁₈	Direct product of C₁₈ and D₉	36	2	D9xC18	324,61
C₂×C₃²⋊C₁₈	Direct product of C₂ and C₃²⋊C₁₈	36	6	C2xC3^2:C18	324,62
C₂×C₉⋊C₁₈	Direct product of C₂ and C₉⋊C₁₈	36	6	C2xC9:C18	324,64
C₂×C₃²⋊₂D₉	Direct product of C₂ and C₃²⋊₂D₉	36	6	C2xC3^2:2D9	324,75
C₂²×C₃≀C₃	Direct product of C₂² and C₃≀C₃	36		C2^2xC3wrC3	324,86
C₃×C₃²⋊C₁₂	Direct product of C₃ and C₃²⋊C₁₂	36	6	C3xC3^2:C12	324,92
Dic₃×He₃	Direct product of Dic₃ and He₃	36	6	Dic3xHe3	324,93
C₃×C₉⋊C₁₂	Direct product of C₃ and C₉⋊C₁₂	36	6	C3xC9:C12	324,94
Dic₃×3_-¹⁺²	Direct product of Dic₃ and 3_-¹⁺²	36	6	Dic3xES-(3,1)	324,95
He₃⋊₆Dic₃	2^nd semidirect product of He₃ and Dic₃ acting via Dic₃/C₆=C₂	36	6	He3:6Dic3	324,104
C₉×C₃²⋊C₄	Direct product of C₉ and C₃²⋊C₄	36	4	C9xC3^2:C4	324,109
C₃²⋊₃Dic₉	The semidirect product of C₃² and Dic₉ acting via Dic₉/C₉=C₄	36	4	C3^2:3Dic9	324,112
C₃×S₃×D₉	Direct product of C₃, S₃ and D₉	36	4	C3xS3xD9	324,114
S₃²×C₉	Direct product of C₉, S₃ and S₃	36	4	S3^2xC9	324,115
C₃²⋊₅D₁₈	2^nd semidirect product of C₃² and D₁₈ acting via D₁₈/C₉=C₂²	36	4	C3^2:5D18	324,123
A₄×He₃	Direct product of A₄ and He₃	36	9	A4xHe3	324,130
A₄×3_-¹⁺²	Direct product of A₄ and 3_-¹⁺²	36	9	A4xES-(3,1)	324,131
C₆×C₃²⋊C₆	Direct product of C₆ and C₃²⋊C₆	36	6	C6xC3^2:C6	324,138
C₂×S₃×He₃	Direct product of C₂, S₃ and He₃	36	6	C2xS3xHe3	324,139
C₆×C₉⋊C₆	Direct product of C₆ and C₉⋊C₆	36	6	C6xC9:C6	324,140
C₂×S₃×3_-¹⁺²	Direct product of C₂, S₃ and 3_-¹⁺²	36	6	C2xS3xES-(3,1)	324,141
C₂×He₃⋊₅S₃	Direct product of C₂ and He₃⋊₅S₃	36	6	C2xHe3:5S3	324,150
C₃²×C₃⋊Dic₃	Direct product of C₃² and C₃⋊Dic₃	36		C3^2xC3:Dic3	324,156
C₃²×C₃²⋊C₄	Direct product of C₃² and C₃²⋊C₄	36		C3^2xC3^2:C4	324,161
C₃⁴⋊C₄	3^rd semidirect product of C₃⁴ and C₄ acting faithfully	36		C3^4:C4	324,163
S₃²×C₃²	Direct product of C₃², S₃ and S₃	36		S3^2xC3^2	324,165
C₃×S₃×C₃⋊S₃	Direct product of C₃, S₃ and C₃⋊S₃	36		C3xS3xC3:S3	324,166
C₃³⋊₁₇D₆	5^th semidirect product of C₃³ and D₆ acting via D₆/C₃=C₂²	36		C3^3:17D6	324,170
C₃⋊S₃×C₃×C₆	Direct product of C₃×C₆ and C₃⋊S₃	36		C3:S3xC3xC6	324,173

Groups of order 432

		d	ρ	Label	ID
C₁₂².C₃	2^nd non-split extension by C₁₂² of C₃ acting faithfully	36	3	C12^2.C3	432,102
C₄²⋊He₃	The semidirect product of C₄² and He₃ acting via He₃/C₃²=C₃	36	3	C4^2:He3	432,103
C₃²⋊D₆⋊C₄	The semidirect product of C₃²⋊D₆ and C₄ acting via C₄/C₂=C₂	36	6	C3^2:D6:C4	432,238
C₆².Dic₃	8^th non-split extension by C₆² of Dic₃ acting via Dic₃/C₂=S₃	36	6-	C6^2.Dic3	432,249
C₃×C₆.S₄	Direct product of C₃ and C₆.S₄	36	6	C3xC6.S4	432,250
C₆²⋊₅Dic₃	4^th semidirect product of C₆² and Dic₃ acting via Dic₃/C₂=S₃	36	6-	C6^2:5Dic3	432,251
C₆²⋊₆Dic₃	5^th semidirect product of C₆² and Dic₃ acting via Dic₃/C₂=S₃	36	3	C6^2:6Dic3	432,260
Dic₃×C₃.A₄	Direct product of Dic₃ and C₃.A₄	36	6	Dic3xC3.A4	432,271
C₆²⋊₄C₁₂	3^rd semidirect product of C₆² and C₁₂ acting via C₁₂/C₂=C₆	36	6-	C6^2:4C12	432,272
C₂²⋊(He₃⋊C₄)	The semidirect product of C₂² and He₃⋊C₄ acting via He₃⋊C₄/He₃⋊C₂=C₂	36	6	C2^2:(He3:C4)	432,279
C₄×C₃²⋊D₆	Direct product of C₄ and C₃²⋊D₆	36	6	C4xC3^2:D6	432,300
C₃⋊S₃⋊D₁₂	The semidirect product of C₃⋊S₃ and D₁₂ acting via D₁₂/C₄=S₃	36	12+	C3:S3:D12	432,301
C₁₂.₈₆S₃²	6^th non-split extension by C₁₂ of S₃² acting via S₃²/C₃⋊S₃=C₂	36	6+	C12.86S3^2	432,302
D₁₈⋊D₆	4^th semidirect product of D₁₈ and D₆ acting via D₆/S₃=C₂	36	4+	D18:D6	432,315
C₆²⋊D₆	1^st semidirect product of C₆² and D₆ acting faithfully	36	12+	C6^2:D6	432,323
C₆²⋊₂D₆	2^nd semidirect product of C₆² and D₆ acting faithfully	36	6	C6^2:2D6	432,324
C₄×C₃².A₄	Direct product of C₄ and C₃².A₄	36	3	C4xC3^2.A4	432,332
C₄×C₃²⋊A₄	Direct product of C₄ and C₃²⋊A₄	36	3	C4xC3^2:A4	432,333
D₄×C₃²⋊C₆	Direct product of D₄ and C₃²⋊C₆	36	12+	D4xC3^2:C6	432,360
D₄×C₉⋊C₆	Direct product of D₄ and C₉⋊C₆; = Aut(D₃₆) = Hol(C₃₆)	36	12+	D4xC9:C6	432,362
D₄×He₃⋊C₂	Direct product of D₄ and He₃⋊C₂	36	6	D4xHe3:C2	432,390
D₉×S₄	Direct product of D₉ and S₄	36	6+	D9xS4	432,521
S₃×C₃.S₄	Direct product of S₃ and C₃.S₄	36	12+	S3xC3.S4	432,522
C₃.A₄²	2^nd central extension by C₃ of A₄²	36	9	C3.A4^2	432,525
C₂⁴⋊He₃	The semidirect product of C₂⁴ and He₃ acting via He₃/C₃=C₃²	36	9	C2^4:He3	432,526
C₂⁴⋊₂3_-¹⁺²	2^nd semidirect product of C₂⁴ and 3_-¹⁺² acting via 3_-¹⁺²/C₃=C₃²	36	9	C2^4:2ES-(3,1)	432,528
C₂×He₃⋊D₄	Direct product of C₂ and He₃⋊D₄	36	6+	C2xHe3:D4	432,530
C₆×C₃.S₄	Direct product of C₆ and C₃.S₄	36	6	C6xC3.S4	432,534
C₂×S₃×C₃.A₄	Direct product of C₂, S₃ and C₃.A₄	36	6	C2xS3xC3.A4	432,541
C₂²×C₃²⋊D₆	Direct product of C₂² and C₃²⋊D₆	36		C2^2xC3^2:D6	432,545
C₂²×C₃².A₄	Direct product of C₂² and C₃².A₄	36		C2^2xC3^2.A4	432,549
C₂²×C₃²⋊A₄	Direct product of C₂² and C₃²⋊A₄	36		C2^2xC3^2:A4	432,550
C₆².A₄	9^th non-split extension by C₆² of A₄ acting via A₄/C₂²=C₃	36		C6^2.A4	432,554
C₆²⋊A₄	2^nd semidirect product of C₆² and A₄ acting via A₄/C₂²=C₃	36		C6^2:A4	432,555
C₃×C₆.₇S₄	Direct product of C₃ and C₆.₇S₄	36	6	C3xC6.7S4	432,618
C₃×Dic₃×A₄	Direct product of C₃, Dic₃ and A₄	36	6	C3xDic3xA4	432,624
C₆²⋊₂₃D₆	4^th semidirect product of C₆² and D₆ acting via D₆/C₃=C₂²	36		C6^2:23D6	432,686
C₃⋊S₃×S₄	Direct product of C₃⋊S₃ and S₄	36		C3:S3xS4	432,746
C₃×A₄²	Direct product of C₃, A₄ and A₄	36	9	C3xA4^2	432,750
C₆×C₃⋊S₄	Direct product of C₆ and C₃⋊S₄	36	6	C6xC3:S4	432,761
S₃×C₆×A₄	Direct product of C₆, S₃ and A₄	36	6	S3xC6xA4	432,763

On 37 points

Groups of order 37

		d	ρ	Label	ID
C₃₇	Cyclic group	37	1	C37	37,1

Groups of order 74

		d	ρ	Label	ID
D₃₇	Dihedral group	37	2+	D37	74,1

Groups of order 111

		d	ρ	Label	ID
C₃₇⋊C₃	The semidirect product of C₃₇ and C₃ acting faithfully	37	3	C37:C3	111,1

Groups of order 148

		d	ρ	Label	ID
C₃₇⋊C₄	The semidirect product of C₃₇ and C₄ acting faithfully	37	4+	C37:C4	148,3

Groups of order 222

		d	ρ	Label	ID
C₃₇⋊C₆	The semidirect product of C₃₇ and C₆ acting faithfully	37	6+	C37:C6	222,1

Groups of order 333

		d	ρ	Label	ID
C₃₇⋊C₉	The semidirect product of C₃₇ and C₉ acting faithfully	37	9	C37:C9	333,3

Groups of order 444

		d	ρ	Label	ID
C₃₇⋊C₁₂	The semidirect product of C₃₇ and C₁₂ acting faithfully	37	12+	C37:C12	444,7

On 38 points

Groups of order 38

		d	ρ	Label	ID
C₃₈	Cyclic group	38	1	C38	38,2

Groups of order 76

		d	ρ	Label	ID
D₃₈	Dihedral group; = C₂×D₁₉	38	2+	D38	76,3

Groups of order 114

		d	ρ	Label	ID
C₂×C₁₉⋊C₃	Direct product of C₂ and C₁₉⋊C₃	38	3	C2xC19:C3	114,2

Groups of order 228

		d	ρ	Label	ID
C₂×C₁₉⋊C₆	Direct product of C₂ and C₁₉⋊C₆	38	6+	C2xC19:C6	228,7

Groups of order 342

		d	ρ	Label	ID
C₂×C₁₉⋊C₉	Direct product of C₂ and C₁₉⋊C₉	38	9	C2xC19:C9	342,8

On 39 points

Groups of order 39

		d	ρ	Label	ID
C₃₉	Cyclic group	39	1	C39	39,2

Groups of order 78

		d	ρ	Label	ID
S₃×C₁₃	Direct product of C₁₃ and S₃	39	2	S3xC13	78,3
C₃×D₁₃	Direct product of C₃ and D₁₃	39	2	C3xD13	78,4
D₃₉	Dihedral group	39	2+	D39	78,5

Groups of order 117

		d	ρ	Label	ID
C₃×C₁₃⋊C₃	Direct product of C₃ and C₁₃⋊C₃	39	3	C3xC13:C3	117,3

Groups of order 156

		d	ρ	Label	ID
C₃×C₁₃⋊C₄	Direct product of C₃ and C₁₃⋊C₄	39	4	C3xC13:C4	156,9
C₃₉⋊C₄	1^st semidirect product of C₃₉ and C₄ acting faithfully	39	4	C39:C4	156,10
S₃×D₁₃	Direct product of S₃ and D₁₃	39	4+	S3xD13	156,11

Groups of order 234

		d	ρ	Label	ID
C₃×C₁₃⋊C₆	Direct product of C₃ and C₁₃⋊C₆	39	6	C3xC13:C6	234,7
S₃×C₁₃⋊C₃	Direct product of S₃ and C₁₃⋊C₃	39	6	S3xC13:C3	234,8
D₃₉⋊C₃	The semidirect product of D₃₉ and C₃ acting faithfully	39	6+	D39:C3	234,9

Groups of order 312

		d	ρ	Label	ID
S₃×C₁₃⋊C₄	Direct product of S₃ and C₁₃⋊C₄	39	8+	S3xC13:C4	312,46

Groups of order 468

		d	ρ	Label	ID
C₃×F₁₃	Direct product of C₃ and F₁₃	39	12	C3xF13	468,29
C₃⋊F₁₃	The semidirect product of C₃ and F₁₃ acting via F₁₃/C₁₃⋊C₆=C₂	39	12	C3:F13	468,30
S₃×C₁₃⋊C₆	Direct product of S₃ and C₁₃⋊C₆	39	12+	S3xC13:C6	468,31

On 40 points

Groups of order 40

		d	ρ	Label	ID
C₅⋊₂C₈	The semidirect product of C₅ and C₈ acting via C₈/C₄=C₂	40	2	C5:2C8	40,1
C₄₀	Cyclic group	40	1	C40	40,2
C₅⋊C₈	The semidirect product of C₅ and C₈ acting via C₈/C₂=C₄	40	4-	C5:C8	40,3
Dic₁₀	Dicyclic group; = C₅ ⋊Q₈	40	2-	Dic10	40,4
C₂×Dic₅	Direct product of C₂ and Dic₅	40		C2xDic5	40,7
C₂×C₂₀	Abelian group of type [2,20]	40		C2xC20	40,9
C₅×Q₈	Direct product of C₅ and Q₈	40	2	C5xQ8	40,11
C₂²×C₁₀	Abelian group of type [2,2,10]	40		C2^2xC10	40,14

Groups of order 80

		d	ρ	Label	ID
C₈×D₅	Direct product of C₈ and D₅	40	2	C8xD5	80,4
C₈⋊D₅	3^rd semidirect product of C₈ and D₅ acting via D₅/C₅=C₂	40	2	C8:D5	80,5
C₄₀⋊C₂	2^nd semidirect product of C₄₀ and C₂ acting faithfully	40	2	C40:C2	80,6
D₄₀	Dihedral group	40	2+	D40	80,7
C₄.Dic₅	The non-split extension by C₄ of Dic₅ acting via Dic₅/C₁₀=C₂	40	2	C4.Dic5	80,10
D₁₀⋊C₄	1^st semidirect product of D₁₀ and C₄ acting via C₄/C₂=C₂	40		D10:C4	80,14
D₄⋊D₅	The semidirect product of D₄ and D₅ acting via D₅/C₅=C₂	40	4+	D4:D5	80,15
D₄.D₅	The non-split extension by D₄ of D₅ acting via D₅/C₅=C₂	40	4-	D4.D5	80,16
Q₈⋊D₅	The semidirect product of Q₈ and D₅ acting via D₅/C₅=C₂	40	4+	Q8:D5	80,17
C₂³.D₅	The non-split extension by C₂³ of D₅ acting via D₅/C₅=C₂	40		C2^3.D5	80,19
C₅×C₂²⋊C₄	Direct product of C₅ and C₂²⋊C₄	40		C5xC2^2:C4	80,21
C₅×M₄(2)	Direct product of C₅ and M₄(2)	40	2	C5xM4(2)	80,24
C₅×D₈	Direct product of C₅ and D₈	40	2	C5xD8	80,25
C₅×SD₁₆	Direct product of C₅ and SD₁₆	40	2	C5xSD16	80,26
D₅⋊C₈	The semidirect product of D₅ and C₈ acting via C₈/C₄=C₂	40	4	D5:C8	80,28
C₄.F₅	The non-split extension by C₄ of F₅ acting via F₅/D₅=C₂	40	4	C4.F5	80,29
C₂².F₅	The non-split extension by C₂² of F₅ acting via F₅/D₅=C₂	40	4-	C2^2.F5	80,33
C₂×C₄×D₅	Direct product of C₂×C₄ and D₅	40		C2xC4xD5	80,36
C₂×D₂₀	Direct product of C₂ and D₂₀	40		C2xD20	80,37
C₄○D₂₀	Central product of C₄ and D₂₀	40	2	C4oD20	80,38
D₄⋊₂D₅	The semidirect product of D₄ and D₅ acting through Inn(D₄)	40	4-	D4:2D5	80,40
Q₈×D₅	Direct product of Q₈ and D₅	40	4-	Q8xD5	80,41
Q₈⋊₂D₅	The semidirect product of Q₈ and D₅ acting through Inn(Q₈)	40	4+	Q8:2D5	80,42
C₂×C₅⋊D₄	Direct product of C₂ and C₅⋊D₄	40		C2xC5:D4	80,44
D₄×C₁₀	Direct product of C₁₀ and D₄	40		D4xC10	80,46
C₅×C₄○D₄	Direct product of C₅ and C₄○D₄	40	2	C5xC4oD4	80,48
C₂³×D₅	Direct product of C₂³ and D₅	40		C2^3xD5	80,51

Groups of order 120

		d	ρ	Label	ID
C₅×SL₂(𝔽₃)	Direct product of C₅ and SL₂(𝔽₃)	40	2	C5xSL(2,3)	120,15

Groups of order 160

		d	ρ	Label	ID
D₂₀⋊₄C₄	1^st semidirect product of D₂₀ and C₄ acting via C₄/C₂=C₂	40	2	D20:4C4	160,12
C₂³.₁D₁₀	1^st non-split extension by C₂³ of D₁₀ acting via D₁₀/C₅=C₂²	40	4	C2^3.1D10	160,13
C₂₀.₄₆D₄	3^rd non-split extension by C₂₀ of D₄ acting via D₄/C₂²=C₂	40	4+	C20.46D4	160,30
D₂₀⋊₇C₄	4^th semidirect product of D₂₀ and C₄ acting via C₄/C₂=C₂	40	4	D20:7C4	160,32
C₂₀.D₄	8^th non-split extension by C₂₀ of D₄ acting via D₄/C₂=C₂²	40	4	C20.D4	160,40
C₂³⋊Dic₅	The semidirect product of C₂³ and Dic₅ acting via Dic₅/C₅=C₄	40	4	C2^3:Dic5	160,41
D₄⋊₂Dic₅	2^nd semidirect product of D₄ and Dic₅ acting via Dic₅/C₁₀=C₂	40	4	D4:2Dic5	160,44
C₅×C₂³⋊C₄	Direct product of C₅ and C₂³⋊C₄	40	4	C5xC2^3:C4	160,49
C₅×C₄.D₄	Direct product of C₅ and C₄.D₄	40	4	C5xC4.D4	160,50
C₅×C₄≀C₂	Direct product of C₅ and C₄≀C₂	40	2	C5xC4wrC2	160,54
C₈×F₅	Direct product of C₈ and F₅	40	4	C8xF5	160,66
C₈⋊F₅	3^rd semidirect product of C₈ and F₅ acting via F₅/D₅=C₂	40	4	C8:F5	160,67
C₄₀⋊C₄	2^nd semidirect product of C₄₀ and C₄ acting faithfully	40	4	C40:C4	160,68
D₅.D₈	The non-split extension by D₅ of D₈ acting via D₈/C₈=C₂	40	4	D5.D8	160,69
D₁₀.D₄	1^st non-split extension by D₁₀ of D₄ acting via D₄/C₂=C₂²	40	4+	D10.D4	160,74
D₁₀.₃Q₈	3^rd non-split extension by D₁₀ of Q₈ acting via Q₈/C₄=C₂	40		D10.3Q8	160,81
D₂₀⋊C₄	1^st semidirect product of D₂₀ and C₄ acting faithfully	40	8+	D20:C4	160,82
D₄⋊F₅	2^nd semidirect product of D₄ and F₅ acting via F₅/D₅=C₂	40	8-	D4:F5	160,83
Q₈⋊F₅	1^st semidirect product of Q₈ and F₅ acting via F₅/D₅=C₂	40	8-	Q8:F5	160,84
Q₈⋊₂F₅	2^nd semidirect product of Q₈ and F₅ acting via F₅/D₅=C₂	40	8+	Q8:2F5	160,85
C₂³⋊F₅	The semidirect product of C₂³ and F₅ acting via F₅/C₅=C₄	40	4	C2^3:F5	160,86
C₂³.F₅	The non-split extension by C₂³ of F₅ acting via F₅/C₅=C₄	40	4	C2^3.F5	160,88
D₅×C₂²⋊C₄	Direct product of D₅ and C₂²⋊C₄	40		D5xC2^2:C4	160,101
C₂²⋊D₂₀	The semidirect product of C₂² and D₂₀ acting via D₂₀/D₁₀=C₂	40		C2^2:D20	160,103
D₅×M₄(2)	Direct product of D₅ and M₄(2)	40	4	D5xM4(2)	160,127
C₈⋊D₁₀	1^st semidirect product of C₈ and D₁₀ acting via D₁₀/C₅=C₂²	40	4+	C8:D10	160,129
D₅×D₈	Direct product of D₅ and D₈	40	4+	D5xD8	160,131
D₈⋊D₅	2^nd semidirect product of D₈ and D₅ acting via D₅/C₅=C₂	40	4	D8:D5	160,132
D₅×SD₁₆	Direct product of D₅ and SD₁₆	40	4	D5xSD16	160,134
D₄₀⋊C₂	6^th semidirect product of D₄₀ and C₂ acting faithfully	40	4+	D40:C2	160,135
D₄.D₁₀	1^st non-split extension by D₄ of D₁₀ acting via D₁₀/C₁₀=C₂	40	4	D4.D10	160,153
C₂³⋊D₁₀	1^st semidirect product of C₂³ and D₁₀ acting via D₁₀/C₅=C₂²	40		C2^3:D10	160,158
D₄⋊D₁₀	2^nd semidirect product of D₄ and D₁₀ acting via D₁₀/C₁₀=C₂	40	4+	D4:D10	160,170
C₂⁴⋊₂D₅	1^st semidirect product of C₂⁴ and D₅ acting via D₅/C₅=C₂	40		C2^4:2D5	160,174
C₅×C₂²≀C₂	Direct product of C₅ and C₂²≀C₂	40		C5xC2^2wrC2	160,181
C₅×C₈⋊C₂²	Direct product of C₅ and C₈⋊C₂²	40	4	C5xC8:C2^2	160,197
D₅⋊M₄(2)	The semidirect product of D₅ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	40	4	D5:M4(2)	160,202
C₂×C₄×F₅	Direct product of C₂×C₄ and F₅	40		C2xC4xF5	160,203
C₂×C₄⋊F₅	Direct product of C₂ and C₄⋊F₅	40		C2xC4:F5	160,204
D₁₀.C₂³	11^st non-split extension by D₁₀ of C₂³ acting via C₂³/C₂²=C₂	40	4	D10.C2^3	160,205
Q₈×F₅	Direct product of Q₈ and F₅	40	8-	Q8xF5	160,209
C₂×C₂²⋊F₅	Direct product of C₂ and C₂²⋊F₅	40		C2xC2^2:F5	160,212
C₂×D₄×D₅	Direct product of C₂, D₄ and D₅	40		C2xD4xD5	160,217
D₄⋊₆D₁₀	2^nd semidirect product of D₄ and D₁₀ acting through Inn(D₄)	40	4	D4:6D10	160,219
D₅×C₄○D₄	Direct product of D₅ and C₄○D₄	40	4	D5xC4oD4	160,223
D₄⋊₈D₁₀	4^th semidirect product of D₄ and D₁₀ acting through Inn(D₄)	40	4+	D4:8D10	160,224
C₅×2₊¹⁺⁴	Direct product of C₅ and 2₊¹⁺⁴	40	4	C5xES+(2,2)	160,232
C₂³×F₅	Direct product of C₂³ and F₅	40		C2^3xF5	160,236

Groups of order 200

		d	ρ	Label	ID
C₅×C₅⋊₂C₈	Direct product of C₅ and C₅⋊₂C₈	40	2	C5xC5:2C8	200,15
C₅×C₅⋊C₈	Direct product of C₅ and C₅⋊C₈	40	4	C5xC5:C8	200,18
C₅²⋊₃C₈	2^nd semidirect product of C₅² and C₈ acting via C₈/C₂=C₄	40	4	C5^2:3C8	200,19
C₅²⋊₅C₈	4^th semidirect product of C₅² and C₈ acting via C₈/C₂=C₄	40	4-	C5^2:5C8	200,21
D₅×Dic₅	Direct product of D₅ and Dic₅	40	4-	D5xDic5	200,22
C₅²⋊₂D₄	1^st semidirect product of C₅² and D₄ acting via D₄/C₂=C₂²	40	4-	C5^2:2D4	200,24
C₅²⋊₂Q₈	The semidirect product of C₅² and Q₈ acting via Q₈/C₂=C₂²	40	4-	C5^2:2Q8	200,26
C₅×Dic₁₀	Direct product of C₅ and Dic₁₀	40	2	C5xDic10	200,27
D₅×C₂₀	Direct product of C₂₀ and D₅	40	2	D5xC20	200,28
C₅×D₂₀	Direct product of C₅ and D₂₀	40	2	C5xD20	200,29
C₁₀×Dic₅	Direct product of C₁₀ and Dic₅	40		C10xDic5	200,30
C₁₀×F₅	Direct product of C₁₀ and F₅	40	4	C10xF5	200,45
C₂×D₅.D₅	Direct product of C₂ and D₅.D₅	40	4	C2xD5.D5	200,46
D₅×C₂×C₁₀	Direct product of C₂×C₁₀ and D₅	40		D5xC2xC10	200,50

Groups of order 240

		d	ρ	Label	ID
C₂.S₅	2^nd central stem extension by C₂ of S₅	40	4-	C2.S5	240,90
C₅×GL₂(𝔽₃)	Direct product of C₅ and GL₂(𝔽₃)	40	2	C5xGL(2,3)	240,103
Q₈⋊D₁₅	The semidirect product of Q₈ and D₁₅ acting via D₁₅/C₅=S₃	40	4+	Q8:D15	240,106
D₅×SL₂(𝔽₃)	Direct product of D₅ and SL₂(𝔽₃)	40	4-	D5xSL(2,3)	240,109

Groups of order 280

		d	ρ	Label	ID
C₅×F₈	Direct product of C₅ and F₈	40	7	C5xF8	280,33

Groups of order 320

		d	ρ	Label	ID
C₅⋊₃C₂≀C₄	The semidirect product of C₅ and C₂≀C₄ acting via C₂≀C₄/C₂³⋊C₄=C₂	40	8+	C5:3C2wrC4	320,29
C₂³.₂D₂₀	2^nd non-split extension by C₂³ of D₂₀ acting via D₂₀/C₅=D₄	40	8+	C2^3.2D20	320,32
C₂³.₃D₂₀	3^rd non-split extension by C₂³ of D₂₀ acting via D₂₀/C₅=D₄	40	8+	C2^3.3D20	320,33
C₂⁴⋊₂Dic₅	1^st semidirect product of C₂⁴ and Dic₅ acting via Dic₅/C₅=C₄	40	4	C2^4:2Dic5	320,94
C₄²⋊₃Dic₅	3^rd semidirect product of C₄² and Dic₅ acting via Dic₅/C₅=C₄	40	4	C4^2:3Dic5	320,103
C₅×C₂≀C₄	Direct product of C₅ and C₂≀C₄	40	4	C5xC2wrC4	320,156
C₅×C₄²⋊C₄	Direct product of C₅ and C₄²⋊C₄	40	4	C5xC4^2:C4	320,158
C₄²⋊F₅	1^st semidirect product of C₄² and F₅ acting via F₅/C₅=C₄	40	4+	C4^2:F5	320,191
C₄²⋊₆F₅	3^rd semidirect product of C₄² and F₅ acting via F₅/D₅=C₂	40	4	C4^2:6F5	320,200
C₅⋊C₂≀C₄	The semidirect product of C₅ and C₂≀C₄ acting via C₂≀C₄/C₂²⋊C₄=C₄	40	8+	C5:C2wrC4	320,202
(C₂²×F₅)⋊C₄	The semidirect product of C₂²×F₅ and C₄ acting faithfully	40	8+	(C2^2xF5):C4	320,204
M₄(2)⋊F₅	2^nd semidirect product of M₄(2) and F₅ acting via F₅/D₅=C₂	40	8	M4(2):F5	320,237
M₄(2)⋊₃F₅	3^rd semidirect product of M₄(2) and F₅ acting via F₅/D₅=C₂	40	8	M4(2):3F5	320,238
(C₂×D₄)⋊F₅	2^nd semidirect product of C₂×D₄ and F₅ acting via F₅/C₅=C₄	40	8+	(C2xD4):F5	320,260
C₂⁴⋊₂F₅	1^st semidirect product of C₂⁴ and F₅ acting via F₅/C₅=C₄	40	4	C2^4:2F5	320,272
C₂³⋊D₂₀	The semidirect product of C₂³ and D₂₀ acting via D₂₀/C₅=D₄	40	8+	C2^3:D20	320,368
D₅×C₂³⋊C₄	Direct product of D₅ and C₂³⋊C₄	40	8+	D5xC2^3:C4	320,370
D₅×C₄.D₄	Direct product of D₅ and C₄.D₄	40	8+	D5xC4.D4	320,371
D₂₀⋊₁D₄	1^st semidirect product of D₂₀ and D₄ acting via D₄/C₂=C₂²	40	8+	D20:1D4	320,374
D₅×C₄≀C₂	Direct product of D₅ and C₄≀C₂	40	4	D5xC4wrC2	320,447
D₄⋊₄D₂₀	3^rd semidirect product of D₄ and D₂₀ acting via D₂₀/D₁₀=C₂	40	4+	D4:4D20	320,449
C₂⁴⋊₂D₁₀	1^st semidirect product of C₂⁴ and D₁₀ acting via D₁₀/C₅=C₂²	40	4	C2^4:2D10	320,659
D₂₀⋊₅D₄	5^th semidirect product of D₂₀ and D₄ acting via D₄/C₂=C₂²	40	4	D20:5D4	320,704
D₂₀⋊₁₈D₄	6^th semidirect product of D₂₀ and D₄ acting via D₄/C₂²=C₂	40	8+	D20:18D4	320,825
2₊¹⁺⁴⋊D₅	1^st semidirect product of 2₊¹⁺⁴ and D₅ acting via D₅/C₅=C₂	40	8+	ES+(2,2):D5	320,868
2₊¹⁺⁴⋊₂D₅	2^nd semidirect product of 2₊¹⁺⁴ and D₅ acting via D₅/C₅=C₂	40	8+	ES+(2,2):2D5	320,871
C₅×D₄⋊₄D₄	Direct product of C₅ and D₄⋊₄D₄	40	4	C5xD4:4D4	320,954
C₅×C₂≀C₂²	Direct product of C₅ and C₂≀C₂²	40	4	C5xC2wrC2^2	320,958
C₂²⋊C₄×F₅	Direct product of C₂²⋊C₄ and F₅	40		C2^2:C4xF5	320,1036
D₁₀⋊(C₄⋊C₄)	The semidirect product of D₁₀ and C₄⋊C₄ acting via C₄⋊C₄/C₂²=C₂²	40		D10:(C4:C4)	320,1037
M₄(2)×F₅	Direct product of M₄(2) and F₅	40	8	M4(2)xF5	320,1064
M₄(2)⋊₁F₅	1^st semidirect product of M₄(2) and F₅ acting via F₅/D₅=C₂	40	8	M4(2):1F5	320,1065
D₈×F₅	Direct product of D₈ and F₅	40	8+	D8xF5	320,1068
D₄₀⋊C₄	2^nd semidirect product of D₄₀ and C₄ acting faithfully	40	8+	D40:C4	320,1069
SD₁₆×F₅	Direct product of SD₁₆ and F₅	40	8	SD16xF5	320,1072
SD₁₆⋊F₅	1^st semidirect product of SD₁₆ and F₅ acting via F₅/D₅=C₂	40	8	SD16:F5	320,1073
(D₄×C₁₀)⋊C₄	6^th semidirect product of D₄×C₁₀ and C₄ acting faithfully	40	8+	(D4xC10):C4	320,1105
(C₂×D₄)⋊₇F₅	5^th semidirect product of C₂×D₄ and F₅ acting via F₅/D₅=C₂	40	8+	(C2xD4):7F5	320,1108
D₅⋊(C₄.D₄)	The semidirect product of D₅ and C₄.D₄ acting via C₄.D₄/C₂×D₄=C₂	40	8+	D5:(C4.D4)	320,1116
(C₂×F₅)⋊D₄	The semidirect product of C₂×F₅ and D₄ acting via D₄/C₂²=C₂	40		(C2xF5):D4	320,1117
D₅⋊C₄≀C₂	The semidirect product of D₅ and C₄≀C₂ acting via C₄≀C₂/C₄○D₄=C₂	40	8	D5:C4wrC2	320,1130
C₄○D₄⋊F₅	2^nd semidirect product of C₄○D₄ and F₅ acting via F₅/D₅=C₂	40	8	C4oD4:F5	320,1131
C₂⁴⋊₄F₅	1^st semidirect product of C₂⁴ and F₅ acting via F₅/D₅=C₂	40		C2^4:4F5	320,1138
D₅×C₂²≀C₂	Direct product of D₅ and C₂²≀C₂	40		D5xC2^2wrC2	320,1260
D₅×C₈⋊C₂²	Direct product of D₅ and C₈⋊C₂²	40	8+	D5xC8:C2^2	320,1444
C₂×D₄×F₅	Direct product of C₂, D₄ and F₅	40		C2xD4xF5	320,1595
D₁₀.C₂⁴	15^th non-split extension by D₁₀ of C₂⁴ acting via C₂⁴/C₂³=C₂	40	8+	D10.C2^4	320,1596
C₄○D₄×F₅	Direct product of C₄○D₄ and F₅	40	8	C4oD4xF5	320,1603
D₅.2₊¹⁺⁴	The non-split extension by D₅ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₄○D₄=C₂	40	8	D5.ES+(2,2)	320,1604
D₅×2₊¹⁺⁴	Direct product of D₅ and 2₊¹⁺⁴	40	8+	D5xES+(2,2)	320,1622

Groups of order 400

		d	ρ	Label	ID
C₂₀.₂₉D₁₀	3^rd non-split extension by C₂₀ of D₁₀ acting via D₁₀/D₅=C₂	40	4	C20.29D10	400,61
C₂₀.₃₁D₁₀	5^th non-split extension by C₂₀ of D₁₀ acting via D₁₀/D₅=C₂	40	4	C20.31D10	400,63
C₅⋊D₄₀	The semidirect product of C₅ and D₄₀ acting via D₄₀/D₂₀=C₂	40	4+	C5:D40	400,65
C₅²⋊₄SD₁₆	3^rd semidirect product of C₅² and SD₁₆ acting via SD₁₆/C₄=C₂²	40	4+	C5^2:4SD16	400,68
C₁₀.D₂₀	6^th non-split extension by C₁₀ of D₂₀ acting via D₂₀/D₁₀=C₂	40		C10.D20	400,73
C₅×C₄.Dic₅	Direct product of C₅ and C₄.Dic₅	40	2	C5xC4.Dic5	400,82
C₅×D₄⋊D₅	Direct product of C₅ and D₄⋊D₅	40	4	C5xD4:D5	400,87
C₅×D₄.D₅	Direct product of C₅ and D₄.D₅	40	4	C5xD4.D5	400,88
C₅×C₂³.D₅	Direct product of C₅ and C₂³.D₅	40		C5xC2^3.D5	400,91
D₅.D₂₀	The non-split extension by D₅ of D₂₀ acting via D₂₀/D₁₀=C₂	40	8+	D5.D20	400,118
Dic₅.₄F₅	The non-split extension by Dic₅ of F₅ acting through Inn(Dic₅)	40	8+	Dic5.4F5	400,121
Dic₅.F₅	1^st non-split extension by Dic₅ of F₅ acting via F₅/D₅=C₂	40	8+	Dic5.F5	400,123
C₅²⋊D₈	The semidirect product of C₅² and D₈ acting via D₈/C₂=D₄	40	4	C5^2:D8	400,131
C₅²⋊SD₁₆	The semidirect product of C₅² and SD₁₆ acting via SD₁₆/C₂=D₄	40	4-	C5^2:SD16	400,132
C₅×C₂².F₅	Direct product of C₅ and C₂².F₅	40	4	C5xC2^2.F5	400,140
C₅×C₂²⋊F₅	Direct product of C₅ and C₂²⋊F₅	40	4	C5xC2^2:F5	400,141
C₁₀².C₄	4^th non-split extension by C₁₀² of C₄ acting faithfully	40	4	C10^2.C4	400,147
D₁₀.D₁₀	5^th non-split extension by D₁₀ of D₁₀ acting via D₁₀/C₁₀=C₂	40	4	D10.D10	400,148
C₂₀.₁₁F₅	11^st non-split extension by C₂₀ of F₅ acting via F₅/C₅=C₄	40	4	C20.11F5	400,156
C₅²⋊₈M₄(2)	4^th semidirect product of C₅² and M₄(2) acting via M₄(2)/C₄=C₄	40	4	C5^2:8M4(2)	400,157
C₄×C₅²⋊C₄	Direct product of C₄ and C₅²⋊C₄	40	4	C4xC5^2:C4	400,158
C₂₀⋊₂F₅	2^nd semidirect product of C₂₀ and F₅ acting via F₅/C₅=C₄	40	4	C20:2F5	400,159
C₅²⋊₁₄M₄(2)	4^th semidirect product of C₅² and M₄(2) acting via M₄(2)/C₂²=C₄	40	4-	C5^2:14M4(2)	400,161
D₂₀⋊D₅	3^rd semidirect product of D₂₀ and D₅ acting via D₅/C₅=C₂	40	4	D20:D5	400,165
Dic₁₀⋊D₅	4^th semidirect product of Dic₁₀ and D₅ acting via D₅/C₅=C₂	40	4	Dic10:D5	400,166
D₁₀.₉D₁₀	1^st non-split extension by D₁₀ of D₁₀ acting via D₁₀/C₁₀=C₂	40	4	D10.9D10	400,167
Dic₁₀⋊₅D₅	The semidirect product of Dic₁₀ and D₅ acting through Inn(Dic₁₀)	40	4+	Dic10:5D5	400,168
C₄×D₅²	Direct product of C₄, D₅ and D₅	40	4	C4xD5^2	400,169
D₅×D₂₀	Direct product of D₅ and D₂₀	40	4+	D5xD20	400,170
C₂₀⋊D₁₀	2^nd semidirect product of C₂₀ and D₁₀ acting via D₁₀/C₅=C₂²	40	4	C20:D10	400,171
Dic₅.D₁₀	3^rd non-split extension by Dic₅ of D₁₀ acting via D₁₀/D₅=C₂	40	4	Dic5.D10	400,173
D₁₀.₄D₁₀	4^th non-split extension by D₁₀ of D₁₀ acting via D₁₀/D₅=C₂	40	4-	D10.4D10	400,174
C₂×Dic₅⋊₂D₅	Direct product of C₂ and Dic₅⋊₂D₅	40		C2xDic5:2D5	400,175
C₂×C₅⋊D₂₀	Direct product of C₂ and C₅⋊D₂₀	40		C2xC5:D20	400,177
D₅×C₅⋊D₄	Direct product of D₅ and C₅⋊D₄	40	4	D5xC5:D4	400,179
C₅×C₄○D₂₀	Direct product of C₅ and C₄○D₂₀	40	2	C5xC4oD20	400,184
C₅×D₄×D₅	Direct product of C₅, D₄ and D₅	40	4	C5xD4xD5	400,185
C₅×D₄⋊₂D₅	Direct product of C₅ and D₄⋊₂D₅	40	4	C5xD4:2D5	400,186
C₁₀×C₅⋊D₄	Direct product of C₁₀ and C₅⋊D₄	40		C10xC5:D4	400,190
C₂×D₅×F₅	Direct product of C₂, D₅ and F₅	40	8+	C2xD5xF5	400,209
C₂²×C₅²⋊C₄	Direct product of C₂² and C₅²⋊C₄	40		C2^2xC5^2:C4	400,217
C₂²×D₅²	Direct product of C₂², D₅ and D₅	40		C2^2xD5^2	400,218

Groups of order 480

		d	ρ	Label	ID
A₅⋊C₈	The semidirect product of A₅ and C₈ acting via C₈/C₄=C₂	40	4	A5:C8	480,217
C₈×A₅	Direct product of C₈ and A₅	40	3	C8xA5	480,220
(C₂²×D₅)⋊A₄	The semidirect product of C₂²×D₅ and A₄ acting faithfully	40	6	(C2^2xD5):A4	480,268
C₅×C₂⁴⋊C₆	Direct product of C₅ and C₂⁴⋊C₆	40	6	C5xC2^4:C6	480,656
C₄.₃S₅	3^rd non-split extension by C₄ of S₅ acting via S₅/A₅=C₂	40	4	C4.3S5	480,948
C₂×C₄×A₅	Direct product of C₂×C₄ and A₅	40		C2xC4xA5	480,954
Q₈×A₅	Direct product of Q₈ and A₅	40	6-	Q8xA5	480,958
D₁₀.S₄	3^rd non-split extension by D₁₀ of S₄ acting via S₄/A₄=C₂	40	8-	D10.S4	480,962
F₅×SL₂(𝔽₃)	Direct product of F₅ and SL₂(𝔽₃)	40	8-	F5xSL(2,3)	480,965
D₅×GL₂(𝔽₃)	Direct product of D₅ and GL₂(𝔽₃)	40	4	D5xGL(2,3)	480,974
C₅×C₂³⋊A₄	Direct product of C₅ and C₂³⋊A₄	40	4	C5xC2^3:A4	480,1134
C₂³×A₅	Direct product of C₂³ and A₅	40		C2^3xA5	480,1187
C₅×C₂²⋊S₄	Direct product of C₅ and C₂²⋊S₄	40	6	C5xC2^2:S4	480,1200
C₂⁴⋊₄D₁₅	3^rd semidirect product of C₂⁴ and D₁₅ acting via D₁₅/C₅=S₃	40	6	C2^4:4D15	480,1201

On 41 points

Groups of order 41

		d	ρ	Label	ID
C₄₁	Cyclic group	41	1	C41	41,1

Groups of order 82

		d	ρ	Label	ID
D₄₁	Dihedral group	41	2+	D41	82,1

Groups of order 164

		d	ρ	Label	ID
C₄₁⋊C₄	The semidirect product of C₄₁ and C₄ acting faithfully	41	4+	C41:C4	164,3

Groups of order 205

		d	ρ	Label	ID
C₄₁⋊C₅	The semidirect product of C₄₁ and C₅ acting faithfully	41	5	C41:C5	205,1

Groups of order 328

		d	ρ	Label	ID
C₄₁⋊C₈	The semidirect product of C₄₁ and C₈ acting faithfully	41	8+	C41:C8	328,12

Groups of order 410

		d	ρ	Label	ID
C₄₁⋊C₁₀	The semidirect product of C₄₁ and C₁₀ acting faithfully	41	10+	C41:C10	410,1

On 42 points

Groups of order 42

		d	ρ	Label	ID
C₄₂	Cyclic group	42	1	C42	42,6

Groups of order 84

		d	ρ	Label	ID
C₆×D₇	Direct product of C₆ and D₇	42	2	C6xD7	84,12
S₃×C₁₄	Direct product of C₁₄ and S₃	42	2	S3xC14	84,13
D₄₂	Dihedral group; = C₂×D₂₁	42	2+	D42	84,14

Groups of order 126

		d	ρ	Label	ID
C₆×C₇⋊C₃	Direct product of C₆ and C₇⋊C₃	42	3	C6xC7:C3	126,10
S₃×C₂₁	Direct product of C₂₁ and S₃	42	2	S3xC21	126,12
C₃×D₂₁	Direct product of C₃ and D₂₁	42	2	C3xD21	126,13

Groups of order 168

		d	ρ	Label	ID
C₂×S₃×D₇	Direct product of C₂, S₃ and D₇	42	4+	C2xS3xD7	168,50
A₄×C₁₄	Direct product of C₁₄ and A₄	42	3	A4xC14	168,52
C₂×C₇⋊A₄	Direct product of C₂ and C₇⋊A₄	42	3	C2xC7:A4	168,53

Groups of order 252

		d	ρ	Label	ID
C₆×F₇	Direct product of C₆ and F₇	42	6	C6xF7	252,28
C₂×S₃×C₇⋊C₃	Direct product of C₂, S₃ and C₇⋊C₃	42	6	C2xS3xC7:C3	252,29
C₂×C₃⋊F₇	Direct product of C₂ and C₃⋊F₇	42	6+	C2xC3:F7	252,30
C₇×C₃²⋊C₄	Direct product of C₇ and C₃²⋊C₄	42	4	C7xC3^2:C4	252,31
C₃²⋊Dic₇	The semidirect product of C₃² and Dic₇ acting via Dic₇/C₇=C₄	42	4	C3^2:Dic7	252,32
C₃×S₃×D₇	Direct product of C₃, S₃ and D₇	42	4	C3xS3xD7	252,33
S₃²×C₇	Direct product of C₇, S₃ and S₃	42	4	S3^2xC7	252,35
S₃×D₂₁	Direct product of S₃ and D₂₁	42	4+	S3xD21	252,36
D₂₁⋊S₃	The semidirect product of D₂₁ and S₃ acting via S₃/C₃=C₂	42	4	D21:S3	252,37

Groups of order 294

		d	ρ	Label	ID
C₇×F₇	Direct product of C₇ and F₇	42	6	C7xF7	294,8
D₇×C₇⋊C₃	Direct product of D₇ and C₇⋊C₃	42	6	D7xC7:C3	294,9
C₇⋊₃F₇	1^st semidirect product of C₇ and F₇ acting via F₇/D₇=C₃	42	6	C7:3F7	294,11
C₁₄×C₇⋊C₃	Direct product of C₁₄ and C₇⋊C₃	42	3	C14xC7:C3	294,15
C₂×C₇²⋊₃C₃	Direct product of C₂ and C₇²⋊₃C₃	42	3	C2xC7^2:3C3	294,17
D₇×C₂₁	Direct product of C₂₁ and D₇	42	2	D7xC21	294,18
C₇×D₂₁	Direct product of C₇ and D₂₁	42	2	C7xD21	294,21

Groups of order 336

		d	ρ	Label	ID
C₆×F₈	Direct product of C₆ and F₈	42	7	C6xF8	336,213
C₁₄×S₄	Direct product of C₁₄ and S₄	42	3	C14xS4	336,214
C₂×C₇⋊S₄	Direct product of C₂ and C₇⋊S₄	42	6+	C2xC7:S4	336,215
C₂×A₄×D₇	Direct product of C₂, A₄ and D₇	42	6+	C2xA4xD7	336,217
C₂×D₇⋊A₄	Direct product of C₂ and D₇⋊A₄	42	6+	C2xD7:A4	336,218

Groups of order 378

		d	ρ	Label	ID
C₃×S₃×C₇⋊C₃	Direct product of C₃, S₃ and C₇⋊C₃	42	6	C3xS3xC7:C3	378,48
C₃×C₃⋊F₇	Direct product of C₃ and C₃⋊F₇	42	6	C3xC3:F7	378,49

On 43 points

Groups of order 43

		d	ρ	Label	ID
C₄₃	Cyclic group	43	1	C43	43,1

Groups of order 86

		d	ρ	Label	ID
D₄₃	Dihedral group	43	2+	D43	86,1

Groups of order 129

		d	ρ	Label	ID
C₄₃⋊C₃	The semidirect product of C₄₃ and C₃ acting faithfully	43	3	C43:C3	129,1

Groups of order 258

		d	ρ	Label	ID
C₄₃⋊C₆	The semidirect product of C₄₃ and C₆ acting faithfully	43	6+	C43:C6	258,1

Groups of order 301

		d	ρ	Label	ID
C₄₃⋊C₇	The semidirect product of C₄₃ and C₇ acting faithfully	43	7	C43:C7	301,1

On 44 points

Groups of order 44

		d	ρ	Label	ID
Dic₁₁	Dicyclic group; = C₁₁ ⋊C₄	44	2-	Dic11	44,1
C₄₄	Cyclic group	44	1	C44	44,2
C₂×C₂₂	Abelian group of type [2,22]	44		C2xC22	44,4

Groups of order 88

		d	ρ	Label	ID
C₄×D₁₁	Direct product of C₄ and D₁₁	44	2	C4xD11	88,4
D₄₄	Dihedral group	44	2+	D44	88,5
C₁₁⋊D₄	The semidirect product of C₁₁ and D₄ acting via D₄/C₂²=C₂	44	2	C11:D4	88,7
D₄×C₁₁	Direct product of C₁₁ and D₄	44	2	D4xC11	88,9
C₂²×D₁₁	Direct product of C₂² and D₁₁	44		C2^2xD11	88,11

Groups of order 132

		d	ρ	Label	ID
C₁₁×A₄	Direct product of C₁₁ and A₄	44	3	C11xA4	132,6

Groups of order 176

		d	ρ	Label	ID
D₄×D₁₁	Direct product of D₄ and D₁₁	44	4+	D4xD11	176,31

Groups of order 220

		d	ρ	Label	ID
C₁₁⋊C₂₀	The semidirect product of C₁₁ and C₂₀ acting via C₂₀/C₂=C₁₀	44	10-	C11:C20	220,1
C₄×C₁₁⋊C₅	Direct product of C₄ and C₁₁⋊C₅	44	5	C4xC11:C5	220,2
C₂²×C₁₁⋊C₅	Direct product of C₂² and C₁₁⋊C₅	44		C2^2xC11:C5	220,8

Groups of order 264

		d	ρ	Label	ID
C₁₁×S₄	Direct product of C₁₁ and S₄	44	3	C11xS4	264,31
C₁₁⋊S₄	The semidirect product of C₁₁ and S₄ acting via S₄/A₄=C₂	44	6+	C11:S4	264,32
A₄×D₁₁	Direct product of A₄ and D₁₁	44	6+	A4xD11	264,33

Groups of order 440

		d	ρ	Label	ID
C₄×F₁₁	Direct product of C₄ and F₁₁	44	10	C4xF11	440,8
D₄₄⋊C₅	The semidirect product of D₄₄ and C₅ acting faithfully	44	10+	D44:C5	440,9
C₂²⋊F₁₁	The semidirect product of C₂² and F₁₁ acting via F₁₁/C₁₁⋊C₅=C₂	44	10	C2^2:F11	440,11
D₄×C₁₁⋊C₅	Direct product of D₄ and C₁₁⋊C₅	44	10	D4xC11:C5	440,13
C₂²×F₁₁	Direct product of C₂² and F₁₁	44		C2^2xF11	440,42

Groups of order 484

		d	ρ	Label	ID
C₁₁×Dic₁₁	Direct product of C₁₁ and Dic₁₁	44	2	C11xDic11	484,5
D₁₁×C₂₂	Direct product of C₂₂ and D₁₁	44	2	D11xC22	484,10

On 45 points

Groups of order 45

		d	ρ	Label	ID
C₄₅	Cyclic group	45	1	C45	45,1
C₃×C₁₅	Abelian group of type [3,15]	45		C3xC15	45,2

Groups of order 90

		d	ρ	Label	ID
C₅×D₉	Direct product of C₅ and D₉	45	2	C5xD9	90,1
C₉×D₅	Direct product of C₉ and D₅	45	2	C9xD5	90,2
D₄₅	Dihedral group	45	2+	D45	90,3
C₃²×D₅	Direct product of C₃² and D₅	45		C3^2xD5	90,5
C₅×C₃⋊S₃	Direct product of C₅ and C₃⋊S₃	45		C5xC3:S3	90,8
C₃⋊D₁₅	The semidirect product of C₃ and D₁₅ acting via D₁₅/C₁₅=C₂	45		C3:D15	90,9

Groups of order 135

		d	ρ	Label	ID
C₅×He₃	Direct product of C₅ and He₃	45	3	C5xHe3	135,3
C₅×3_-¹⁺²	Direct product of C₅ and 3_-¹⁺²	45	3	C5xES-(3,1)	135,4

Groups of order 180

		d	ρ	Label	ID
C₉×F₅	Direct product of C₉ and F₅	45	4	C9xF5	180,5
C₉⋊F₅	The semidirect product of C₉ and F₅ acting via F₅/D₅=C₂	45	4	C9:F5	180,6
D₅×D₉	Direct product of D₅ and D₉	45	4+	D5xD9	180,7
C₃²×F₅	Direct product of C₃² and F₅	45		C3^2xF5	180,20
C₃²⋊₃F₅	2^nd semidirect product of C₃² and F₅ acting via F₅/D₅=C₂	45		C3^2:3F5	180,22
D₅×C₃⋊S₃	Direct product of D₅ and C₃⋊S₃	45		D5xC3:S3	180,27

Groups of order 225

		d	ρ	Label	ID
C₅²⋊C₉	The semidirect product of C₅² and C₉ acting via C₉/C₃=C₃	45	3	C5^2:C9	225,3
C₃×C₅²⋊C₃	Direct product of C₃ and C₅²⋊C₃	45	3	C3xC5^2:C3	225,5

Groups of order 270

		d	ρ	Label	ID
D₅×He₃	Direct product of D₅ and He₃	45	6	D5xHe3	270,6
D₅×3_-¹⁺²	Direct product of D₅ and 3_-¹⁺²	45	6	D5xES-(3,1)	270,7
C₅×C₃²⋊C₆	Direct product of C₅ and C₃²⋊C₆	45	6	C5xC3^2:C6	270,10
C₅×C₉⋊C₆	Direct product of C₅ and C₉⋊C₆	45	6	C5xC9:C6	270,11
He₃⋊D₅	1^st semidirect product of He₃ and D₅ acting via D₅/C₅=C₂	45	6+	He3:D5	270,14
D₄₅⋊C₃	The semidirect product of D₄₅ and C₃ acting faithfully	45	6+	D45:C3	270,15
C₅×He₃⋊C₂	Direct product of C₅ and He₃⋊C₂	45	3	C5xHe3:C2	270,17
C₃²⋊D₁₅	2^nd semidirect product of C₃² and D₁₅ acting via D₁₅/C₅=S₃	45	6	C3^2:D15	270,19

Groups of order 360

		d	ρ	Label	ID
D₉×F₅	Direct product of D₉ and F₅	45	8+	D9xF5	360,39
C₅×F₉	Direct product of C₅ and F₉	45	8	C5xF9	360,123
C₅⋊₂F₉	The semidirect product of C₅ and F₉ acting via F₉/C₃²⋊C₄=C₂	45	8	C5:2F9	360,124
C₅⋊F₉	The semidirect product of C₅ and F₉ acting via F₉/C₃⋊S₃=C₄	45	8	C5:F9	360,125
C₃⋊S₃×F₅	Direct product of C₃⋊S₃ and F₅	45		C3:S3xF5	360,127
C₅×PSU₃(𝔽₂)	Direct product of C₅ and PSU₃(𝔽₂)	45	8	C5xPSU(3,2)	360,135
C₃²⋊Dic₁₀	The semidirect product of C₃² and Dic₁₀ acting via Dic₁₀/C₅=Q₈	45	8	C3^2:Dic10	360,136

Groups of order 405

		d	ρ	Label	ID
C₅×C₃≀C₃	Direct product of C₅ and C₃≀C₃	45	3	C5xC3wrC3	405,7

Groups of order 450

		d	ρ	Label	ID
C₅²⋊D₉	The semidirect product of C₅² and D₉ acting via D₉/C₃=S₃	45	6+	C5^2:D9	450,11
C₅²⋊C₁₈	The semidirect product of C₅² and C₁₈ acting via C₁₈/C₃=C₆	45	6	C5^2:C18	450,12
C₃×C₅²⋊S₃	Direct product of C₃ and C₅²⋊S₃	45	3	C3xC5^2:S3	450,20
C₅²⋊(C₃⋊S₃)	The semidirect product of C₅² and C₃⋊S₃ acting via C₃⋊S₃/C₃=S₃	45	6+	C5^2:(C3:S3)	450,21
C₃×C₅²⋊C₆	Direct product of C₃ and C₅²⋊C₆	45	6	C3xC5^2:C6	450,22
S₃×C₅²⋊C₃	Direct product of S₃ and C₅²⋊C₃	45	6	S3xC5^2:C3	450,23
C₅⋊D₁₅⋊C₃	The semidirect product of C₅⋊D₁₅ and C₃ acting faithfully	45	6+	C5:D15:C3	450,24

On 46 points

Groups of order 46

		d	ρ	Label	ID
C₄₆	Cyclic group	46	1	C46	46,2

Groups of order 92

		d	ρ	Label	ID
D₄₆	Dihedral group; = C₂×D₂₃	46	2+	D46	92,3

On 47 points

Groups of order 47

		d	ρ	Label	ID
C₄₇	Cyclic group	47	1	C47	47,1

Groups of order 94

		d	ρ	Label	ID
D₄₇	Dihedral group	47	2+	D47	94,1

On 48 points

Groups of order 48

		d	ρ	Label	ID
C₃⋊C₁₆	The semidirect product of C₃ and C₁₆ acting via C₁₆/C₈=C₂	48	2	C3:C16	48,1
C₄₈	Cyclic group	48	1	C48	48,2
Dic₁₂	Dicyclic group; = C₃ ⋊₁ Q₁₆	48	2-	Dic12	48,8
C₂×C₃⋊C₈	Direct product of C₂ and C₃⋊C₈	48		C2xC3:C8	48,9
C₄×Dic₃	Direct product of C₄ and Dic₃	48		C4xDic3	48,11
Dic₃⋊C₄	The semidirect product of Dic₃ and C₄ acting via C₄/C₂=C₂	48		Dic3:C4	48,12
C₄⋊Dic₃	The semidirect product of C₄ and Dic₃ acting via Dic₃/C₆=C₂	48		C4:Dic3	48,13
C₃⋊Q₁₆	The semidirect product of C₃ and Q₁₆ acting via Q₁₆/Q₈=C₂	48	4-	C3:Q16	48,18
C₄×C₁₂	Abelian group of type [4,12]	48		C4xC12	48,20
C₃×C₄⋊C₄	Direct product of C₃ and C₄⋊C₄	48		C3xC4:C4	48,22
C₂×C₂₄	Abelian group of type [2,24]	48		C2xC24	48,23
C₃×Q₁₆	Direct product of C₃ and Q₁₆	48	2	C3xQ16	48,27
C₂×Dic₆	Direct product of C₂ and Dic₆	48		C2xDic6	48,34
C₂²×Dic₃	Direct product of C₂² and Dic₃	48		C2^2xDic3	48,42
C₂²×C₁₂	Abelian group of type [2,2,12]	48		C2^2xC12	48,44
C₆×Q₈	Direct product of C₆ and Q₈	48		C6xQ8	48,46
C₂³×C₆	Abelian group of type [2,2,2,6]	48		C2^3xC6	48,52

Groups of order 96

		d	ρ	Label	ID
S₃×C₁₆	Direct product of C₁₆ and S₃	48	2	S3xC16	96,4
D₆.C₈	The non-split extension by D₆ of C₈ acting via C₈/C₄=C₂	48	2	D6.C8	96,5
D₄₈	Dihedral group	48	2+	D48	96,6
C₄₈⋊C₂	2^nd semidirect product of C₄₈ and C₂ acting faithfully	48	2	C48:C2	96,7
C₆.D₈	2^nd non-split extension by C₆ of D₈ acting via D₈/D₄=C₂	48		C6.D8	96,16
C₁₂.C₈	1^st non-split extension by C₁₂ of C₈ acting via C₈/C₄=C₂	48	2	C12.C8	96,19
C₂₄.C₄	1^st non-split extension by C₂₄ of C₄ acting via C₄/C₂=C₂	48	2	C24.C4	96,26
D₆⋊C₈	The semidirect product of D₆ and C₈ acting via C₈/C₄=C₂	48		D6:C8	96,27
C₂.D₂₄	2^nd central extension by C₂ of D₂₄	48		C2.D24	96,28
C₁₂.₅₃D₄	10^th non-split extension by C₁₂ of D₄ acting via D₄/C₂²=C₂	48	4	C12.53D4	96,29
C₁₂.₄₇D₄	4^th non-split extension by C₁₂ of D₄ acting via D₄/C₂²=C₂	48	4-	C12.47D4	96,31
C₃⋊D₁₆	The semidirect product of C₃ and D₁₆ acting via D₁₆/D₈=C₂	48	4+	C3:D16	96,33
D₈.S₃	The non-split extension by D₈ of S₃ acting via S₃/C₃=C₂	48	4-	D8.S3	96,34
C₈.₆D₆	3^rd non-split extension by C₈ of D₆ acting via D₆/S₃=C₂	48	4+	C8.6D6	96,35
C₁₂.₅₅D₄	12^nd non-split extension by C₁₂ of D₄ acting via D₄/C₂²=C₂	48		C12.55D4	96,37
D₄⋊Dic₃	1^st semidirect product of D₄ and Dic₃ acting via Dic₃/C₆=C₂	48		D4:Dic3	96,39
C₁₂.₁₀D₄	10^th non-split extension by C₁₂ of D₄ acting via D₄/C₂=C₂²	48	4	C12.10D4	96,43
C₃×C₂²⋊C₈	Direct product of C₃ and C₂²⋊C₈	48		C3xC2^2:C8	96,48
C₃×C₄.₁₀D₄	Direct product of C₃ and C₄.₁₀D₄	48	4	C3xC4.10D4	96,51
C₃×D₄⋊C₄	Direct product of C₃ and D₄⋊C₄	48		C3xD4:C4	96,52
C₃×C₈.C₄	Direct product of C₃ and C₈.C₄	48	2	C3xC8.C4	96,58
C₃×M₅(2)	Direct product of C₃ and M₅(2)	48	2	C3xM5(2)	96,60
C₃×D₁₆	Direct product of C₃ and D₁₆	48	2	C3xD16	96,61
C₃×SD₃₂	Direct product of C₃ and SD₃₂	48	2	C3xSD32	96,62
S₃×C₄²	Direct product of C₄² and S₃	48		S3xC4^2	96,78
C₄²⋊₂S₃	1^st semidirect product of C₄² and S₃ acting via S₃/C₃=C₂	48		C4^2:2S3	96,79
C₄×D₁₂	Direct product of C₄ and D₁₂	48		C4xD12	96,80
C₄⋊D₁₂	The semidirect product of C₄ and D₁₂ acting via D₁₂/C₁₂=C₂	48		C4:D12	96,81
C₄²⋊₇S₃	6^th semidirect product of C₄² and S₃ acting via S₃/C₃=C₂	48		C4^2:7S3	96,82
C₄²⋊₃S₃	2^nd semidirect product of C₄² and S₃ acting via S₃/C₃=C₂	48		C4^2:3S3	96,83
C₂³.₁₆D₆	1^st non-split extension by C₂³ of D₆ acting via D₆/S₃=C₂	48		C2^3.16D6	96,84
Dic₃.D₄	1^st non-split extension by Dic₃ of D₄ acting via D₄/C₂²=C₂	48		Dic3.D4	96,85
C₂³.₈D₆	3^rd non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	48		C2^3.8D6	96,86
Dic₃⋊₄D₄	1^st semidirect product of Dic₃ and D₄ acting through Inn(Dic₃)	48		Dic3:4D4	96,88
C₂³.₉D₆	4^th non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	48		C2^3.9D6	96,90
Dic₃⋊D₄	1^st semidirect product of Dic₃ and D₄ acting via D₄/C₂²=C₂	48		Dic3:D4	96,91
C₂³.₁₁D₆	6^th non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	48		C2^3.11D6	96,92
C₂³.₂₁D₆	6^th non-split extension by C₂³ of D₆ acting via D₆/S₃=C₂	48		C2^3.21D6	96,93
S₃×C₄⋊C₄	Direct product of S₃ and C₄⋊C₄	48		S3xC4:C4	96,98
C₄⋊C₄⋊₇S₃	1^st semidirect product of C₄⋊C₄ and S₃ acting through Inn(C₄⋊C₄)	48		C4:C4:7S3	96,99
Dic₃⋊₅D₄	2^nd semidirect product of Dic₃ and D₄ acting through Inn(Dic₃)	48		Dic3:5D4	96,100
D₆.D₄	2^nd non-split extension by D₆ of D₄ acting via D₄/C₂²=C₂	48		D6.D4	96,101
C₁₂⋊D₄	1^st semidirect product of C₁₂ and D₄ acting via D₄/C₂=C₂²	48		C12:D4	96,102
D₆⋊Q₈	1^st semidirect product of D₆ and Q₈ acting via Q₈/C₄=C₂	48		D6:Q8	96,103
C₄.D₁₂	5^th non-split extension by C₄ of D₁₂ acting via D₁₂/D₆=C₂	48		C4.D12	96,104
C₄⋊C₄⋊S₃	6^th semidirect product of C₄⋊C₄ and S₃ acting via S₃/C₃=C₂	48		C4:C4:S3	96,105
S₃×C₂×C₈	Direct product of C₂×C₈ and S₃	48		S3xC2xC8	96,106
C₂×C₈⋊S₃	Direct product of C₂ and C₈⋊S₃	48		C2xC8:S3	96,107
C₈○D₁₂	Central product of C₈ and D₁₂	48	2	C8oD12	96,108
C₂×C₂₄⋊C₂	Direct product of C₂ and C₂₄⋊C₂	48		C2xC24:C2	96,109
C₂×D₂₄	Direct product of C₂ and D₂₄	48		C2xD24	96,110
C₄○D₂₄	Central product of C₄ and D₂₄	48	2	C4oD24	96,111
D₁₂.C₄	The non-split extension by D₁₂ of C₄ acting via C₄/C₂=C₂	48	4	D12.C4	96,114
C₈.D₆	1^st non-split extension by C₈ of D₆ acting via D₆/C₃=C₂²	48	4-	C8.D6	96,116
D₈⋊₃S₃	The semidirect product of D₈ and S₃ acting through Inn(D₈)	48	4-	D8:3S3	96,119
D₄.D₆	4^th non-split extension by D₄ of D₆ acting via D₆/S₃=C₂	48	4-	D4.D6	96,122
Q₈.₇D₆	2^nd non-split extension by Q₈ of D₆ acting via D₆/S₃=C₂	48	4	Q8.7D6	96,123
S₃×Q₁₆	Direct product of S₃ and Q₁₆	48	4-	S3xQ16	96,124
Q₁₆⋊S₃	2^nd semidirect product of Q₁₆ and S₃ acting via S₃/C₃=C₂	48	4	Q16:S3	96,125
D₂₄⋊C₂	5^th semidirect product of D₂₄ and C₂ acting faithfully	48	4+	D24:C2	96,126
C₂×C₄.Dic₃	Direct product of C₂ and C₄.Dic₃	48		C2xC4.Dic3	96,128
C₁₂.₄₈D₄	5^th non-split extension by C₁₂ of D₄ acting via D₄/C₂²=C₂	48		C12.48D4	96,131
C₂³.₂₆D₆	2^nd non-split extension by C₂³ of D₆ acting via D₆/C₆=C₂	48		C2^3.26D6	96,133
C₂×D₆⋊C₄	Direct product of C₂ and D₆⋊C₄	48		C2xD6:C4	96,134
C₄×C₃⋊D₄	Direct product of C₄ and C₃⋊D₄	48		C4xC3:D4	96,135
C₂³.₂₈D₆	4^th non-split extension by C₂³ of D₆ acting via D₆/C₆=C₂	48		C2^3.28D6	96,136
C₁₂⋊₇D₄	1^st semidirect product of C₁₂ and D₄ acting via D₄/C₂²=C₂	48		C12:7D4	96,137
C₂×D₄⋊S₃	Direct product of C₂ and D₄⋊S₃	48		C2xD4:S3	96,138
C₂×D₄.S₃	Direct product of C₂ and D₄.S₃	48		C2xD4.S3	96,140
D₄×Dic₃	Direct product of D₄ and Dic₃	48		D4xDic3	96,141
C₂³.₂₃D₆	8^th non-split extension by C₂³ of D₆ acting via D₆/S₃=C₂	48		C2^3.23D6	96,142
C₂³.₁₂D₆	7^th non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	48		C2^3.12D6	96,143
D₆⋊₃D₄	3^rd semidirect product of D₆ and D₄ acting via D₄/C₄=C₂	48		D6:3D4	96,145
C₂³.₁₄D₆	9^th non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	48		C2^3.14D6	96,146
C₁₂⋊₃D₄	3^rd semidirect product of C₁₂ and D₄ acting via D₄/C₂=C₂²	48		C12:3D4	96,147
C₂×Q₈⋊₂S₃	Direct product of C₂ and Q₈⋊₂S₃	48		C2xQ8:2S3	96,148
Q₈.₁₁D₆	1^st non-split extension by Q₈ of D₆ acting via D₆/C₆=C₂	48	4	Q8.11D6	96,149
D₆⋊₃Q₈	3^rd semidirect product of D₆ and Q₈ acting via Q₈/C₄=C₂	48		D6:3Q8	96,153
C₁₂.₂₃D₄	23^rd non-split extension by C₁₂ of D₄ acting via D₄/C₂=C₂²	48		C12.23D4	96,154
D₄.Dic₃	The non-split extension by D₄ of Dic₃ acting through Inn(D₄)	48	4	D4.Dic3	96,155
Q₈.₁₃D₆	3^rd non-split extension by Q₈ of D₆ acting via D₆/C₆=C₂	48	4	Q8.13D6	96,157
Q₈.₁₄D₆	4^th non-split extension by Q₈ of D₆ acting via D₆/C₆=C₂	48	4-	Q8.14D6	96,158
C₂×C₆.D₄	Direct product of C₂ and C₆.D₄	48		C2xC6.D4	96,159
C₆×C₂²⋊C₄	Direct product of C₆ and C₂²⋊C₄	48		C6xC2^2:C4	96,162
C₃×C₄²⋊C₂	Direct product of C₃ and C₄²⋊C₂	48		C3xC4^2:C2	96,164
D₄×C₁₂	Direct product of C₁₂ and D₄	48		D4xC12	96,165
C₃×C₄⋊D₄	Direct product of C₃ and C₄⋊D₄	48		C3xC4:D4	96,168
C₃×C₂²⋊Q₈	Direct product of C₃ and C₂²⋊Q₈	48		C3xC2^2:Q8	96,169
C₃×C₂².D₄	Direct product of C₃ and C₂².D₄	48		C3xC2^2.D4	96,170
C₃×C₄.₄D₄	Direct product of C₃ and C₄.₄D₄	48		C3xC4.4D4	96,171
C₃×C₄²⋊₂C₂	Direct product of C₃ and C₄²⋊₂C₂	48		C3xC4^2:2C2	96,173
C₃×C₄⋊₁D₄	Direct product of C₃ and C₄⋊₁D₄	48		C3xC4:1D4	96,174
C₆×M₄(2)	Direct product of C₆ and M₄(2)	48		C6xM4(2)	96,177
C₃×C₈○D₄	Direct product of C₃ and C₈○D₄	48	2	C3xC8oD4	96,178
C₆×D₈	Direct product of C₆ and D₈	48		C6xD8	96,179
C₆×SD₁₆	Direct product of C₆ and SD₁₆	48		C6xSD16	96,180
C₃×C₄○D₈	Direct product of C₃ and C₄○D₈	48	2	C3xC4oD8	96,182
C₃×C₈.C₂²	Direct product of C₃ and C₈.C₂²	48	4	C3xC8.C2^2	96,184
S₃×C₂²×C₄	Direct product of C₂²×C₄ and S₃	48		S3xC2^2xC4	96,206
C₂²×D₁₂	Direct product of C₂² and D₁₂	48		C2^2xD12	96,207
C₂×C₄○D₁₂	Direct product of C₂ and C₄○D₁₂	48		C2xC4oD12	96,208
C₂×D₄⋊₂S₃	Direct product of C₂ and D₄⋊₂S₃	48		C2xD4:2S3	96,210
C₂×S₃×Q₈	Direct product of C₂, S₃ and Q₈	48		C2xS3xQ8	96,212
C₂×Q₈⋊₃S₃	Direct product of C₂ and Q₈⋊₃S₃	48		C2xQ8:3S3	96,213
Q₈.₁₅D₆	1^st non-split extension by Q₈ of D₆ acting through Inn(Q₈)	48	4	Q8.15D6	96,214
Q₈○D₁₂	Central product of Q₈ and D₁₂	48	4-	Q8oD12	96,217
C₂²×C₃⋊D₄	Direct product of C₂² and C₃⋊D₄	48		C2^2xC3:D4	96,219
D₄×C₂×C₆	Direct product of C₂×C₆ and D₄	48		D4xC2xC6	96,221
C₆×C₄○D₄	Direct product of C₆ and C₄○D₄	48		C6xC4oD4	96,223
C₃×2_-¹⁺⁴	Direct product of C₃ and 2_-¹⁺⁴	48	4	C3xES-(2,2)	96,225
S₃×C₂⁴	Direct product of C₂⁴ and S₃	48		S3xC2^4	96,230

Groups of order 144

		d	ρ	Label	ID
C₃×C₃⋊C₁₆	Direct product of C₃ and C₃⋊C₁₆	48	2	C3xC3:C16	144,28
C₃²⋊₂C₁₆	The semidirect product of C₃² and C₁₆ acting via C₁₆/C₄=C₄	48	4	C3^2:2C16	144,51
S₃×C₃⋊C₈	Direct product of S₃ and C₃⋊C₈	48	4	S3xC3:C8	144,52
D₆.Dic₃	The non-split extension by D₆ of Dic₃ acting via Dic₃/C₆=C₂	48	4	D6.Dic3	144,54
C₃²⋊₂D₈	1^st semidirect product of C₃² and D₈ acting via D₈/C₄=C₂²	48	4	C3^2:2D8	144,56
Dic₆⋊S₃	2^nd semidirect product of Dic₆ and S₃ acting via S₃/C₃=C₂	48	4	Dic6:S3	144,58
D₁₂.S₃	1^st non-split extension by D₁₂ of S₃ acting via S₃/C₃=C₂	48	4-	D12.S3	144,59
C₃²⋊₂Q₁₆	1^st semidirect product of C₃² and Q₁₆ acting via Q₁₆/C₄=C₂²	48	4	C3^2:2Q16	144,61
C₃²⋊₃Q₁₆	2^nd semidirect product of C₃² and Q₁₆ acting via Q₁₆/C₄=C₂²	48	4-	C3^2:3Q16	144,62
Dic₃²	Direct product of Dic₃ and Dic₃	48		Dic3^2	144,63
D₆⋊Dic₃	The semidirect product of D₆ and Dic₃ acting via Dic₃/C₆=C₂	48		D6:Dic3	144,64
Dic₃⋊Dic₃	The semidirect product of Dic₃ and Dic₃ acting via Dic₃/C₆=C₂	48		Dic3:Dic3	144,66
C₆².C₂²	5^th non-split extension by C₆² of C₂² acting faithfully	48		C6^2.C2^2	144,67
S₃×C₂₄	Direct product of C₂₄ and S₃	48	2	S3xC24	144,69
C₃×C₈⋊S₃	Direct product of C₃ and C₈⋊S₃	48	2	C3xC8:S3	144,70
C₃×C₂₄⋊C₂	Direct product of C₃ and C₂₄⋊C₂	48	2	C3xC24:C2	144,71
C₃×D₂₄	Direct product of C₃ and D₂₄	48	2	C3xD24	144,72
C₃×Dic₁₂	Direct product of C₃ and Dic₁₂	48	2	C3xDic12	144,73
C₆×C₃⋊C₈	Direct product of C₆ and C₃⋊C₈	48		C6xC3:C8	144,74
Dic₃×C₁₂	Direct product of C₁₂ and Dic₃	48		Dic3xC12	144,76
C₃×Dic₃⋊C₄	Direct product of C₃ and Dic₃⋊C₄	48		C3xDic3:C4	144,77
C₃×C₄⋊Dic₃	Direct product of C₃ and C₄⋊Dic₃	48		C3xC4:Dic3	144,78
C₃×D₆⋊C₄	Direct product of C₃ and D₆⋊C₄	48		C3xD6:C4	144,79
C₃×Q₈⋊₂S₃	Direct product of C₃ and Q₈⋊₂S₃	48	4	C3xQ8:2S3	144,82
C₃×C₃⋊Q₁₆	Direct product of C₃ and C₃⋊Q₁₆	48	4	C3xC3:Q16	144,83
C₂.F₉	The central extension by C₂ of F₉	48	8-	C2.F9	144,114
C₃²⋊Q₁₆	The semidirect product of C₃² and Q₁₆ acting via Q₁₆/C₂=D₄	48	4-	C3^2:Q16	144,119
C₃×CSU₂(𝔽₃)	Direct product of C₃ and CSU₂(𝔽₃)	48	2	C3xCSU(2,3)	144,121
C₆.₅S₄	5^th non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	48	4-	C6.5S4	144,124
Dic₃.A₄	The non-split extension by Dic₃ of A₄ acting through Inn(Dic₃)	48	4+	Dic3.A4	144,127
C₂×C₃²⋊₂C₈	Direct product of C₂ and C₃²⋊₂C₈	48		C2xC3^2:2C8	144,134
S₃×Dic₆	Direct product of S₃ and Dic₆	48	4-	S3xDic6	144,137
D₁₂⋊₅S₃	The semidirect product of D₁₂ and S₃ acting through Inn(D₁₂)	48	4-	D12:5S3	144,138
C₂×S₃×Dic₃	Direct product of C₂, S₃ and Dic₃	48		C2xS3xDic3	144,146
C₂×D₆⋊S₃	Direct product of C₂ and D₆⋊S₃	48		C2xD6:S3	144,150
C₂×C₃²⋊₂Q₈	Direct product of C₂ and C₃²⋊₂Q₈	48		C2xC3^2:2Q8	144,152
C₆×SL₂(𝔽₃)	Direct product of C₆ and SL₂(𝔽₃)	48		C6xSL(2,3)	144,156
C₃×C₄.A₄	Direct product of C₃ and C₄.A₄	48	2	C3xC4.A4	144,157
C₆×Dic₆	Direct product of C₆ and Dic₆	48		C6xDic6	144,158
S₃×C₂×C₁₂	Direct product of C₂×C₁₂ and S₃	48		S3xC2xC12	144,159
C₆×D₁₂	Direct product of C₆ and D₁₂	48		C6xD12	144,160
C₃×S₃×Q₈	Direct product of C₃, S₃ and Q₈	48	4	C3xS3xQ8	144,164
C₃×Q₈⋊₃S₃	Direct product of C₃ and Q₈⋊₃S₃	48	4	C3xQ8:3S3	144,165
Dic₃×C₂×C₆	Direct product of C₂×C₆ and Dic₃	48		Dic3xC2xC6	144,166
S₃×C₂²×C₆	Direct product of C₂²×C₆ and S₃	48		S3xC2^2xC6	144,195

Groups of order 192

		d	ρ	Label	ID
C₆.C₄≀C₂	1^st non-split extension by C₆ of C₄≀C₂ acting via C₄≀C₂/C₄²=C₂	48		C6.C4wrC2	192,10
C₄⋊Dic₃⋊C₄	2^nd semidirect product of C₄⋊Dic₃ and C₄ acting faithfully	48		C4:Dic3:C4	192,11
C₂₄.₁C₈	1^st non-split extension by C₂₄ of C₈ acting via C₈/C₄=C₂	48	2	C24.1C8	192,22
C₁₂.₁₅C₄²	8^th non-split extension by C₁₂ of C₄² acting via C₄²/C₂×C₄=C₂	48	4	C12.15C4^2	192,25
C₂³.₃₅D₁₂	1^st non-split extension by C₂³ of D₁₂ acting via D₁₂/D₆=C₂	48		C2^3.35D12	192,26
(C₂²×S₃)⋊C₈	The semidirect product of C₂²×S₃ and C₈ acting via C₈/C₂=C₄	48		(C2^2xS3):C8	192,27
C₂².₂D₂₄	1^st non-split extension by C₂² of D₂₄ acting via D₂₄/D₁₂=C₂	48		C2^2.2D24	192,29
(C₂×D₄).D₆	2^nd non-split extension by C₂×D₄ of D₆ acting via D₆/C₃=C₂²	48	8-	(C2xD4).D6	192,31
C₂³.D₁₂	1^st non-split extension by C₂³ of D₁₂ acting via D₁₂/C₃=D₄	48	8-	C2^3.D12	192,32
C₂³.₄D₁₂	4^th non-split extension by C₂³ of D₁₂ acting via D₁₂/C₃=D₄	48	8-	C2^3.4D12	192,35
(C₂×C₄).D₁₂	3^rd non-split extension by C₂×C₄ of D₁₂ acting via D₁₂/C₃=D₄	48	8+	(C2xC4).D12	192,36
(C₂×C₁₂).D₄	16^th non-split extension by C₂×C₁₂ of D₄ acting faithfully	48	8-	(C2xC12).D4	192,37
C₈.Dic₆	1^st non-split extension by C₈ of Dic₆ acting via Dic₆/C₆=C₂²	48	4	C8.Dic6	192,46
D₂₄⋊₈C₄	8^th semidirect product of D₂₄ and C₄ acting via C₄/C₂=C₂	48	4	D24:8C4	192,47
C₂₄.₆Q₈	6^th non-split extension by C₂₄ of Q₈ acting via Q₈/C₂=C₂²	48	4	C24.6Q8	192,53
D₂₄.C₄	4^th non-split extension by D₂₄ of C₄ acting via C₄/C₂=C₂	48	4+	D24.C4	192,54
C₂₄.₉₇D₄	20^th non-split extension by C₂₄ of D₄ acting via D₄/C₂²=C₂	48	4	C24.97D4	192,70
C₄₈⋊C₄	2^nd semidirect product of C₄₈ and C₄ acting faithfully	48	4	C48:C4	192,71
C₂₄.Q₈	1^st non-split extension by C₂₄ of Q₈ acting via Q₈/C₂=C₂²	48	4	C24.Q8	192,72
C₈.₂₅D₁₂	11^st non-split extension by C₈ of D₁₂ acting via D₁₂/D₆=C₂	48	4	C8.25D12	192,73
M₅(2)⋊S₃	5^th semidirect product of M₅(2) and S₃ acting via S₃/C₃=C₂	48	4+	M5(2):S3	192,75
D₂₄⋊₂C₄	2^nd semidirect product of D₂₄ and C₄ acting via C₄/C₂=C₂	48	4	D24:2C4	192,77
C₁₂.₈C₄²	1^st non-split extension by C₁₂ of C₄² acting via C₄²/C₂×C₄=C₂	48		C12.8C4^2	192,82
C₂⁴.₃Dic₃	1^st non-split extension by C₂⁴ of Dic₃ acting via Dic₃/C₃=C₄	48		C2^4.3Dic3	192,84
C₂⁴.₁₂D₆	1^st non-split extension by C₂⁴ of D₆ acting via D₆/C₃=C₂²	48		C2^4.12D6	192,85
C₂⁴.₁₃D₆	2^nd non-split extension by C₂⁴ of D₆ acting via D₆/C₃=C₂²	48		C2^4.13D6	192,86
C₄²⋊₃Dic₃	1^st semidirect product of C₄² and Dic₃ acting via Dic₃/C₃=C₄	48	4	C4^2:3Dic3	192,90
C₁₂.₂C₄²	2^nd non-split extension by C₁₂ of C₄² acting via C₄²/C₂²=C₂²	48		C12.2C4^2	192,91
(C₂×C₁₂).Q₈	8^th non-split extension by C₂×C₁₂ of Q₈ acting via Q₈/C₂=C₂²	48	4	(C2xC12).Q8	192,92
(C₆×D₄)⋊C₄	1^st semidirect product of C₆×D₄ and C₄ acting faithfully	48		(C6xD4):C4	192,96
(C₆×Q₈)⋊C₄	1^st semidirect product of C₆×Q₈ and C₄ acting faithfully	48		(C6xQ8):C4	192,97
(C₂²×C₁₂)⋊C₄	2^nd semidirect product of C₂²×C₁₂ and C₄ acting faithfully	48	4	(C2^2xC12):C4	192,98
C₄²⋊₄Dic₃	2^nd semidirect product of C₄² and Dic₃ acting via Dic₃/C₃=C₄	48	4	C4^2:4Dic3	192,100
C₄².Dic₃	2^nd non-split extension by C₄² of Dic₃ acting via Dic₃/C₃=C₄	48	4	C4^2.Dic3	192,101
C₄².₃Dic₃	3^rd non-split extension by C₄² of Dic₃ acting via Dic₃/C₃=C₄	48	4	C4^2.3Dic3	192,107
C₂₄.D₄	52^nd non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	48	4	C24.D4	192,112
C₁₂.₃C₄²	3^rd non-split extension by C₁₂ of C₄² acting via C₄²/C₂²=C₂²	48		C12.3C4^2	192,114
(C₂×C₂₄)⋊C₄	1^st semidirect product of C₂×C₂₄ and C₄ acting faithfully	48	4	(C2xC24):C4	192,115
C₁₂.₂₀C₄²	13^rd non-split extension by C₁₂ of C₄² acting via C₄²/C₂×C₄=C₂	48	4	C12.20C4^2	192,116
M₄(2)⋊₄Dic₃	4^th semidirect product of M₄(2) and Dic₃ acting via Dic₃/C₆=C₂	48	4	M4(2):4Dic3	192,118
C₁₂.₂₁C₄²	14^th non-split extension by C₁₂ of C₄² acting via C₄²/C₂×C₄=C₂	48	4	C12.21C4^2	192,119
D₈.Dic₃	2^nd non-split extension by D₈ of Dic₃ acting via Dic₃/C₆=C₂	48	4	D8.Dic3	192,122
D₈⋊₂Dic₃	2^nd semidirect product of D₈ and Dic₃ acting via Dic₃/C₆=C₂	48	4	D8:2Dic3	192,125
C₃×C₂³⋊C₈	Direct product of C₃ and C₂³⋊C₈	48		C3xC2^3:C8	192,129
C₃×C₂².SD₁₆	Direct product of C₃ and C₂².SD₁₆	48		C3xC2^2.SD16	192,133
C₃×C₂³.₃₁D₄	Direct product of C₃ and C₂³.₃₁D₄	48		C3xC2^3.31D4	192,134
C₃×C₄.₉C₄²	Direct product of C₃ and C₄.₉C₄²	48	4	C3xC4.9C4^2	192,143
C₃×C₄.₁₀C₄²	Direct product of C₃ and C₄.₁₀C₄²	48	4	C3xC4.10C4^2	192,144
C₃×C₄²⋊₆C₄	Direct product of C₃ and C₄²⋊₆C₄	48		C3xC4^2:6C4	192,145
C₃×C₂³.₉D₄	Direct product of C₃ and C₂³.₉D₄	48		C3xC2^3.9D4	192,148
C₃×M₄(2)⋊₄C₄	Direct product of C₃ and M₄(2)⋊₄C₄	48	4	C3xM4(2):4C4	192,150
C₃×C₁₆⋊C₄	Direct product of C₃ and C₁₆⋊C₄	48	4	C3xC16:C4	192,153
C₃×C₂³.C₈	Direct product of C₃ and C₂³.C₈	48	4	C3xC2^3.C8	192,155
C₃×C₂³.D₄	Direct product of C₃ and C₂³.D₄	48	4	C3xC2^3.D4	192,158
C₃×C₄²⋊₃C₄	Direct product of C₃ and C₄²⋊₃C₄	48	4	C3xC4^2:3C4	192,160
C₃×C₄².C₄	Direct product of C₃ and C₄².C₄	48	4	C3xC4^2.C4	192,161
C₃×C₄².₃C₄	Direct product of C₃ and C₄².₃C₄	48	4	C3xC4^2.3C4	192,162
C₃×D₈⋊₂C₄	Direct product of C₃ and D₈⋊₂C₄	48	4	C3xD8:2C4	192,166
C₃×M₅(2)⋊C₂	Direct product of C₃ and M₅(2)⋊C₂	48	4	C3xM5(2):C2	192,167
C₃×C₈.C₈	Direct product of C₃ and C₈.C₈	48	2	C3xC8.C8	192,170
C₃×C₈.Q₈	Direct product of C₃ and C₈.Q₈	48	4	C3xC8.Q8	192,171
A₄⋊C₁₆	The semidirect product of A₄ and C₁₆ acting via C₁₆/C₈=C₂	48	3	A4:C16	192,186
A₄×C₁₆	Direct product of C₁₆ and A₄	48	3	A4xC16	192,203
D₂₄⋊₁₁C₄	The semidirect product of D₂₄ and C₄ acting through Inn(D₂₄)	48	2	D24:11C4	192,259
D₂₄⋊₄C₄	4^th semidirect product of D₂₄ and C₄ acting via C₄/C₂=C₂	48	4	D24:4C4	192,276
S₃×C₂²⋊C₈	Direct product of S₃ and C₂²⋊C₈	48		S3xC2^2:C8	192,283
D₆⋊M₄(2)	1^st semidirect product of D₆ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	48		D6:M4(2)	192,285
D₁₂.₃₁D₄	1^st non-split extension by D₁₂ of D₄ acting via D₄/C₂²=C₂	48		D12.31D4	192,290
D₁₂⋊₁₃D₄	1^st semidirect product of D₁₂ and D₄ acting via D₄/C₂²=C₂	48		D12:13D4	192,291
C₂³⋊C₄⋊₅S₃	The semidirect product of C₂³⋊C₄ and S₃ acting through Inn(C₂³⋊C₄)	48	8-	C2^3:C4:5S3	192,299
C₂³.₅D₁₂	5^th non-split extension by C₂³ of D₁₂ acting via D₁₂/C₃=D₄	48	8-	C2^3.5D12	192,301
M₄(2).₁₉D₆	2^nd non-split extension by M₄(2) of D₆ acting via D₆/S₃=C₂	48	8-	M4(2).19D6	192,304
M₄(2)⋊D₆	1^st semidirect product of M₄(2) and D₆ acting via D₆/C₃=C₂²	48	8-	M4(2):D6	192,305
D₁₂.₂D₄	2^nd non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	48	8-	D12.2D4	192,307
D₁₂.₃D₄	3^rd non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	48	8+	D12.3D4	192,308
S₃×C₄.₁₀D₄	Direct product of S₃ and C₄.₁₀D₄	48	8-	S3xC4.10D4	192,309
M₄(2).₂₁D₆	4^th non-split extension by M₄(2) of D₆ acting via D₆/S₃=C₂	48	8+	M4(2).21D6	192,310
D₁₂.₄D₄	4^th non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	48	8-	D12.4D4	192,311
D₁₂.₅D₄	5^th non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	48	8+	D12.5D4	192,312
D₁₂.₆D₄	6^th non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	48	8+	D12.6D4	192,313
S₃×D₄⋊C₄	Direct product of S₃ and D₄⋊C₄	48		S3xD4:C4	192,328
C₄⋊C₄⋊₁₉D₆	2^nd semidirect product of C₄⋊C₄ and D₆ acting via D₆/S₃=C₂	48		C4:C4:19D6	192,329
D₄⋊D₁₂	1^st semidirect product of D₄ and D₁₂ acting via D₁₂/D₆=C₂	48		D4:D12	192,332
D₆⋊₅SD₁₆	1^st semidirect product of D₆ and SD₁₆ acting via SD₁₆/D₄=C₂	48		D6:5SD16	192,335
C₄²⋊₃D₆	1^st semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48	4	C4^2:3D6	192,380
M₄(2).₂₂D₆	5^th non-split extension by M₄(2) of D₆ acting via D₆/S₃=C₂	48	4	M4(2).22D6	192,382
C₄².₁₉₆D₆	16^th non-split extension by C₄² of D₆ acting via D₆/S₃=C₂	48	4	C4^2.196D6	192,383
C₄²⋊₅D₆	3^rd semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48	4	C4^2:5D6	192,384
Q₈.₁₄D₁₂	4^th non-split extension by Q₈ of D₁₂ acting via D₁₂/D₆=C₂	48	4-	Q8.14D12	192,385
D₄.₁₀D₁₂	5^th non-split extension by D₄ of D₁₂ acting via D₁₂/D₆=C₂	48	4	D4.10D12	192,386
S₃×C₈.C₄	Direct product of S₃ and C₈.C₄	48	4	S3xC8.C4	192,451
M₄(2).₂₅D₆	8^th non-split extension by M₄(2) of D₆ acting via D₆/S₃=C₂	48	4	M4(2).25D6	192,452
D₂₄⋊₁₀C₄	10^th semidirect product of D₂₄ and C₄ acting via C₄/C₂=C₂	48	4	D24:10C4	192,453
D₂₄⋊₇C₄	7^th semidirect product of D₂₄ and C₄ acting via C₄/C₂=C₂	48	4	D24:7C4	192,454
C₂₄.₁₉D₄	19^th non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	48	4+	C24.19D4	192,456
C₂₄.₄₂D₄	42^nd non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	48	4	C24.42D4	192,457
S₃×M₅(2)	Direct product of S₃ and M₅(2)	48	4	S3xM5(2)	192,465
C₁₆⋊D₆	1^st semidirect product of C₁₆ and D₆ acting via D₆/C₃=C₂²	48	4+	C16:D6	192,467
S₃×D₁₆	Direct product of S₃ and D₁₆	48	4+	S3xD16	192,469
D₈⋊D₆	2^nd semidirect product of D₈ and D₆ acting via D₆/S₃=C₂	48	4	D8:D6	192,470
S₃×SD₃₂	Direct product of S₃ and SD₃₂	48	4	S3xSD32	192,472
D₄₈⋊C₂	6^th semidirect product of D₄₈ and C₂ acting faithfully	48	4+	D48:C2	192,473
C₂×C₄²⋊₄S₃	Direct product of C₂ and C₄²⋊₄S₃	48		C2xC4^2:4S3	192,486
C₂×C₂³.₆D₆	Direct product of C₂ and C₂³.₆D₆	48		C2xC2^3.6D6	192,513
C₂⁴.₅₉D₆	6^th non-split extension by C₂⁴ of D₆ acting via D₆/S₃=C₂	48		C2^4.59D6	192,514
C₄⋊C₄⋊₃₆D₆	2^nd semidirect product of C₄⋊C₄ and D₆ acting via D₆/C₆=C₂	48		C4:C4:36D6	192,560
C₄²⋊₆D₆	4^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48	4	C4^2:6D6	192,564
(C₂×D₁₂)⋊₁₃C₄	9^th semidirect product of C₂×D₁₂ and C₄ acting via C₄/C₂=C₂	48	4	(C2xD12):13C4	192,565
D₁₂⋊₁₆D₄	4^th semidirect product of D₁₂ and D₄ acting via D₄/C₂²=C₂	48		D12:16D4	192,595
D₁₂.₃₆D₄	6^th non-split extension by D₁₂ of D₄ acting via D₄/C₂²=C₂	48		D12.36D4	192,605
C₂²⋊C₄⋊D₆	4^th semidirect product of C₂²⋊C₄ and D₆ acting via D₆/C₃=C₂²	48	4	C2^2:C4:D6	192,612
C₄²⋊₇D₆	5^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48	4	C4^2:7D6	192,620
D₁₂.₁₄D₄	14^th non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	48	4	D12.14D4	192,621
D₁₂.₁₅D₄	15^th non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	48	4	D12.15D4	192,654
C₂³.₈Dic₆	6^th non-split extension by C₂³ of Dic₆ acting via Dic₆/C₆=C₂²	48	4	C2^3.8Dic6	192,683
C₂³.₉Dic₆	7^th non-split extension by C₂³ of Dic₆ acting via Dic₆/C₆=C₂²	48	4	C2^3.9Dic6	192,684
D₆⋊₆M₄(2)	2^nd semidirect product of D₆ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	48		D6:6M4(2)	192,685
C₂×C₁₂.₄₆D₄	Direct product of C₂ and C₁₂.₄₆D₄	48		C2xC12.46D4	192,689
C₂³.₅₃D₁₂	19^th non-split extension by C₂³ of D₁₂ acting via D₁₂/D₆=C₂	48		C2^3.53D12	192,690
M₄(2).₃₁D₆	4^th non-split extension by M₄(2) of D₆ acting via D₆/C₆=C₂	48	4	M4(2).31D6	192,691
C₂×D₁₂⋊C₄	Direct product of C₂ and D₁₂⋊C₄	48		C2xD12:C4	192,697
M₄(2)⋊₂₄D₆	8^th semidirect product of M₄(2) and D₆ acting via D₆/C₆=C₂	48	4	M4(2):24D6	192,698
Q₈.₈D₁₂	3^rd non-split extension by Q₈ of D₁₂ acting via D₁₂/C₁₂=C₂	48	4	Q8.8D12	192,700
Q₈.₉D₁₂	4^th non-split extension by Q₈ of D₁₂ acting via D₁₂/C₁₂=C₂	48	4+	Q8.9D12	192,701
C₂₄.₁₀₀D₄	23^rd non-split extension by C₂₄ of D₄ acting via D₄/C₂²=C₂	48	4	C24.100D4	192,703
C₂₄.₅₄D₄	54^th non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	48	4	C24.54D4	192,704
D₈.D₆	1^st non-split extension by D₈ of D₆ acting via D₆/C₆=C₂	48	4	D8.D6	192,706
D₁₂⋊D₄	6^th semidirect product of D₁₂ and D₄ acting via D₄/C₂=C₂²	48		D12:D4	192,715
C₂₄.₂₃D₄	23^rd non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	48	4	C24.23D4	192,719
D₆⋊₆SD₁₆	2^nd semidirect product of D₆ and SD₁₆ acting via SD₁₆/D₄=C₂	48		D6:6SD16	192,728
C₂₄.₄₄D₄	44^th non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	48	4	C24.44D4	192,736
Q₁₆⋊D₆	2^nd semidirect product of Q₁₆ and D₆ acting via D₆/C₆=C₂	48	4+	Q16:D6	192,752
D₈⋊₅Dic₃	The semidirect product of D₈ and Dic₃ acting through Inn(D₈)	48	4	D8:5Dic3	192,755
D₈⋊₄Dic₃	4^th semidirect product of D₈ and Dic₃ acting via Dic₃/C₆=C₂	48	4	D8:4Dic3	192,756
M₄(2).D₆	12^nd non-split extension by M₄(2) of D₆ acting via D₆/C₃=C₂²	48	8+	M4(2).D6	192,758
M₄(2).₁₃D₆	13^rd non-split extension by M₄(2) of D₆ acting via D₆/C₃=C₂²	48	8-	M4(2).13D6	192,759
D₁₂.₃₈D₄	8^th non-split extension by D₁₂ of D₄ acting via D₄/C₂²=C₂	48	8-	D12.38D4	192,760
D₁₂.₃₉D₄	9^th non-split extension by D₁₂ of D₄ acting via D₄/C₂²=C₂	48	8+	D12.39D4	192,761
M₄(2).₁₅D₆	15^th non-split extension by M₄(2) of D₆ acting via D₆/C₃=C₂²	48	8+	M4(2).15D6	192,762
D₁₂.₄₀D₄	10^th non-split extension by D₁₂ of D₄ acting via D₄/C₂²=C₂	48	8-	D12.40D4	192,764
C₂⁴.₆Dic₃	2^nd non-split extension by C₂⁴ of Dic₃ acting via Dic₃/C₆=C₂	48		C2^4.6Dic3	192,766
(C₆×D₄)⋊₆C₄	2^nd semidirect product of C₆×D₄ and C₄ acting via C₄/C₂=C₂	48		(C6xD4):6C4	192,774
C₂×C₁₂.D₄	Direct product of C₂ and C₁₂.D₄	48		C2xC12.D4	192,775
(C₂×C₆)⋊₈D₈	2^nd semidirect product of C₂×C₆ and D₈ acting via D₈/D₄=C₂	48		(C2xC6):8D8	192,776
(C₃×D₄).₃₁D₄	1^st non-split extension by C₃×D₄ of D₄ acting via D₄/C₂²=C₂	48		(C3xD4).31D4	192,777
C₂×C₂³.₇D₆	Direct product of C₂ and C₂³.₇D₆	48		C2xC2^3.7D6	192,778
C₂×Q₈⋊₃Dic₃	Direct product of C₂ and Q₈⋊₃Dic₃	48		C2xQ8:3Dic3	192,794
(C₆×D₄)⋊₉C₄	5^th semidirect product of C₆×D₄ and C₄ acting via C₄/C₂=C₂	48	4	(C6xD4):9C4	192,795
(C₆×D₄).₁₆C₄	10^th non-split extension by C₆×D₄ of C₄ acting via C₄/C₂=C₂	48	4	(C6xD4).16C4	192,796
(C₆×D₄)⋊₁₀C₄	6^th semidirect product of C₆×D₄ and C₄ acting via C₄/C₂=C₂	48	4	(C6xD4):10C4	192,799
2₊¹⁺⁴.₄S₃	1^st non-split extension by 2₊¹⁺⁴ of S₃ acting via S₃/C₃=C₂	48	8-	ES+(2,2).4S3	192,801
2₊¹⁺⁴.₅S₃	2^nd non-split extension by 2₊¹⁺⁴ of S₃ acting via S₃/C₃=C₂	48	8-	ES+(2,2).5S3	192,802
2_-¹⁺⁴⋊₄S₃	1^st semidirect product of 2_-¹⁺⁴ and S₃ acting via S₃/C₃=C₂	48	8+	ES-(2,2):4S3	192,804
2_-¹⁺⁴.₂S₃	The non-split extension by 2_-¹⁺⁴ of S₃ acting via S₃/C₃=C₂	48	8-	ES-(2,2).2S3	192,805
C₂⁵.₄S₃	1^st non-split extension by C₂⁵ of S₃ acting via S₃/C₃=C₂	48		C2^5.4S3	192,806
C₃×C₂⁴⋊₃C₄	Direct product of C₃ and C₂⁴⋊₃C₄	48		C3xC2^4:3C4	192,812
C₃×C₂⁴.₄C₄	Direct product of C₃ and C₂⁴.₄C₄	48		C3xC2^4.4C4	192,840
C₆×C₂³⋊C₄	Direct product of C₆ and C₂³⋊C₄	48		C6xC2^3:C4	192,842
C₃×C₂³.C₂³	Direct product of C₃ and C₂³.C₂³	48	4	C3xC2^3.C2^3	192,843
C₆×C₄.D₄	Direct product of C₆ and C₄.D₄	48		C6xC4.D4	192,844
C₃×M₄(2).₈C₂²	Direct product of C₃ and M₄(2).₈C₂²	48	4	C3xM4(2).8C2^2	192,846
C₃×C₂³.₃₇D₄	Direct product of C₃ and C₂³.₃₇D₄	48		C3xC2^3.37D4	192,851
C₆×C₄≀C₂	Direct product of C₆ and C₄≀C₂	48		C6xC4wrC2	192,853
C₃×C₄²⋊C₂²	Direct product of C₃ and C₄²⋊C₂²	48	4	C3xC4^2:C2^2	192,854
C₃×M₄(2).C₄	Direct product of C₃ and M₄(2).C₄	48	4	C3xM4(2).C4	192,863
C₃×C₈○D₈	Direct product of C₃ and C₈○D₈	48	2	C3xC8oD8	192,876
C₃×C₈.₂₆D₄	Direct product of C₃ and C₈.₂₆D₄	48	4	C3xC8.26D4	192,877
C₃×C₂²⋊D₈	Direct product of C₃ and C₂²⋊D₈	48		C3xC2^2:D8	192,880
C₃×C₂²⋊SD₁₆	Direct product of C₃ and C₂²⋊SD₁₆	48		C3xC2^2:SD16	192,883
C₃×D₄.₈D₄	Direct product of C₃ and D₄.₈D₄	48	4	C3xD4.8D4	192,887
C₃×D₄.₉D₄	Direct product of C₃ and D₄.₉D₄	48	4	C3xD4.9D4	192,888
C₃×D₄.₁₀D₄	Direct product of C₃ and D₄.₁₀D₄	48	4	C3xD4.10D4	192,889
C₃×C₂³.₇D₄	Direct product of C₃ and C₂³.₇D₄	48	4	C3xC2^3.7D4	192,891
C₃×D₄.₃D₄	Direct product of C₃ and D₄.₃D₄	48	4	C3xD4.3D4	192,904
C₃×D₄.₄D₄	Direct product of C₃ and D₄.₄D₄	48	4	C3xD4.4D4	192,905
C₃×C₁₆⋊C₂²	Direct product of C₃ and C₁₆⋊C₂²	48	4	C3xC16:C2^2	192,942
A₄⋊Q₁₆	The semidirect product of A₄ and Q₁₆ acting via Q₁₆/C₈=C₂	48	6-	A4:Q16	192,957
C₂×A₄⋊C₈	Direct product of C₂ and A₄⋊C₈	48		C2xA4:C8	192,967
C₄×A₄⋊C₄	Direct product of C₄ and A₄⋊C₄	48		C4xA4:C4	192,969
C₂⁴.₃D₆	2^nd non-split extension by C₂⁴ of D₆ acting via D₆/C₂=S₃	48		C2^4.3D6	192,970
C₂⁴.₄D₆	3^rd non-split extension by C₂⁴ of D₆ acting via D₆/C₂=S₃	48		C2^4.4D6	192,971
A₄⋊₂Q₁₆	The semidirect product of A₄ and Q₁₆ acting via Q₁₆/Q₈=C₂	48	6-	A4:2Q16	192,975
C₂×U₂(𝔽₃)	Direct product of C₂ and U₂(𝔽₃)	48		C2xU(2,3)	192,981
Q₈.₄S₄	2^nd non-split extension by Q₈ of S₄ acting via S₄/A₄=C₂	48	4	Q8.4S4	192,987
A₄×C₄²	Direct product of C₄² and A₄	48		A4xC4^2	192,993
A₄×C₄⋊C₄	Direct product of A₄ and C₄⋊C₄	48		A4xC4:C4	192,995
A₄×C₂×C₈	Direct product of C₂×C₈ and A₄	48		A4xC2xC8	192,1010
A₄×Q₁₆	Direct product of A₄ and Q₁₆	48	6-	A4xQ16	192,1016
Q₁₆.A₄	The non-split extension by Q₁₆ of A₄ acting through Inn(Q₁₆)	48	4+	Q16.A4	192,1017
C₄².A₄	The non-split extension by C₄² of A₄ acting faithfully	48	12-	C4^2.A4	192,1025
C₂³⋊₃Dic₆	2^nd semidirect product of C₂³ and Dic₆ acting via Dic₆/C₆=C₂²	48		C2^3:3Dic6	192,1042
C₂×S₃×C₂²⋊C₄	Direct product of C₂, S₃ and C₂²⋊C₄	48		C2xS3xC2^2:C4	192,1043
C₂⁴.₃₅D₆	24^th non-split extension by C₂⁴ of D₆ acting via D₆/C₃=C₂²	48		C2^4.35D6	192,1045
C₂×D₆⋊D₄	Direct product of C₂ and D₆⋊D₄	48		C2xD6:D4	192,1046
C₂⁴.₃₈D₆	27^th non-split extension by C₂⁴ of D₆ acting via D₆/C₃=C₂²	48		C2^4.38D6	192,1049
C₂³⋊₄D₁₂	2^nd semidirect product of C₂³ and D₁₂ acting via D₁₂/C₆=C₂²	48		C2^3:4D12	192,1052
C₂⁴.₄₁D₆	30^th non-split extension by C₂⁴ of D₆ acting via D₆/C₃=C₂²	48		C2^4.41D6	192,1053
C₂⁴.₄₂D₆	31^st non-split extension by C₂⁴ of D₆ acting via D₆/C₃=C₂²	48		C2^4.42D6	192,1054
S₃×C₄²⋊C₂	Direct product of S₃ and C₄²⋊C₂	48		S3xC4^2:C2	192,1079
C₄²⋊₉D₆	7^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:9D6	192,1080
C₄²⋊₁₀D₆	8^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:10D6	192,1083
C₄²⋊₁₁D₆	9^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:11D6	192,1084
C₄²⋊₁₂D₆	10^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:12D6	192,1086
C₄×S₃×D₄	Direct product of C₄, S₃ and D₄	48		C4xS3xD4	192,1103
C₄²⋊₁₃D₆	11^st semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:13D6	192,1104
C₄²⋊₁₄D₆	12^nd semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:14D6	192,1106
D₄×D₁₂	Direct product of D₄ and D₁₂	48		D4xD12	192,1108
D₁₂⋊₂₃D₄	1^st semidirect product of D₁₂ and D₄ acting through Inn(D₁₂)	48		D12:23D4	192,1109
D₄⋊₅D₁₂	1^st semidirect product of D₄ and D₁₂ acting through Inn(D₄)	48		D4:5D12	192,1113
C₄²⋊₁₈D₆	16^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:18D6	192,1115
C₄²⋊₁₉D₆	17^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:19D6	192,1119
C₂⁴.₆₇D₆	14^th non-split extension by C₂⁴ of D₆ acting via D₆/S₃=C₂	48		C2^4.67D6	192,1145
C₂⁴.₄₃D₆	32^nd non-split extension by C₂⁴ of D₆ acting via D₆/C₃=C₂²	48		C2^4.43D6	192,1146
C₂⁴⋊₇D₆	2^nd semidirect product of C₂⁴ and D₆ acting via D₆/C₃=C₂²	48		C2^4:7D6	192,1148
C₂⁴⋊₈D₆	3^rd semidirect product of C₂⁴ and D₆ acting via D₆/C₃=C₂²	48		C2^4:8D6	192,1149
C₂⁴.₄₄D₆	33^rd non-split extension by C₂⁴ of D₆ acting via D₆/C₃=C₂²	48		C2^4.44D6	192,1150
C₂⁴.₄₅D₆	34^th non-split extension by C₂⁴ of D₆ acting via D₆/C₃=C₂²	48		C2^4.45D6	192,1151
C₂⁴.₄₆D₆	35^th non-split extension by C₂⁴ of D₆ acting via D₆/C₃=C₂²	48		C2^4.46D6	192,1152
C₂⁴⋊₉D₆	4^th semidirect product of C₂⁴ and D₆ acting via D₆/C₃=C₂²	48		C2^4:9D6	192,1153
C₂⁴.₄₇D₆	36^th non-split extension by C₂⁴ of D₆ acting via D₆/C₃=C₂²	48		C2^4.47D6	192,1154
S₃×C₄⋊D₄	Direct product of S₃ and C₄⋊D₄	48		S3xC4:D4	192,1163
C₆.₃₇2₊¹⁺⁴	37^th non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	48		C6.37ES+(2,2)	192,1164
C₄⋊C₄⋊₂₁D₆	4^th semidirect product of C₄⋊C₄ and D₆ acting via D₆/S₃=C₂	48		C4:C4:21D6	192,1165
C₆.₃₈2₊¹⁺⁴	38^th non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	48		C6.38ES+(2,2)	192,1166
D₁₂⋊₁₉D₄	7^th semidirect product of D₁₂ and D₄ acting via D₄/C₂²=C₂	48		D12:19D4	192,1168
C₆.₄₀2₊¹⁺⁴	40^th non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	48		C6.40ES+(2,2)	192,1169
D₁₂⋊₂₀D₄	8^th semidirect product of D₁₂ and D₄ acting via D₄/C₂²=C₂	48		D12:20D4	192,1171
C₆.₄₂2₊¹⁺⁴	42^nd non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	48		C6.42ES+(2,2)	192,1172
C₆.₄₆2₊¹⁺⁴	46^th non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	48		C6.46ES+(2,2)	192,1176
C₆.₄₈2₊¹⁺⁴	48^th non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	48		C6.48ES+(2,2)	192,1179
S₃×C₂²⋊Q₈	Direct product of S₃ and C₂²⋊Q₈	48		S3xC2^2:Q8	192,1185
C₄⋊C₄⋊₂₆D₆	9^th semidirect product of C₄⋊C₄ and D₆ acting via D₆/S₃=C₂	48		C4:C4:26D6	192,1186
D₁₂⋊₂₁D₄	9^th semidirect product of D₁₂ and D₄ acting via D₄/C₂²=C₂	48		D12:21D4	192,1189
C₆.₅₁2₊¹⁺⁴	51^st non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	48		C6.51ES+(2,2)	192,1193
C₆.₅₃2₊¹⁺⁴	53^rd non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	48		C6.53ES+(2,2)	192,1196
C₆.₅₆2₊¹⁺⁴	56^th non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	48		C6.56ES+(2,2)	192,1203
S₃×C₂².D₄	Direct product of S₃ and C₂².D₄	48		S3xC2^2.D4	192,1211
C₆.₁₂₀2₊¹⁺⁴	29^th non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₄○D₄=C₂	48		C6.120ES+(2,2)	192,1212
C₆.₁₂₁2₊¹⁺⁴	30^th non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₄○D₄=C₂	48		C6.121ES+(2,2)	192,1213
C₄⋊C₄⋊₂₈D₆	11^st semidirect product of C₄⋊C₄ and D₆ acting via D₆/S₃=C₂	48		C4:C4:28D6	192,1215
C₆.₆₁2₊¹⁺⁴	61^st non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	48		C6.61ES+(2,2)	192,1216
C₆.₁₂₂2₊¹⁺⁴	31^st non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₄○D₄=C₂	48		C6.122ES+(2,2)	192,1217
C₆.₆₂2₊¹⁺⁴	62^nd non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	48		C6.62ES+(2,2)	192,1218
C₆.₆₈2₊¹⁺⁴	68^th non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂×D₄=C₂	48		C6.68ES+(2,2)	192,1225
S₃×C₄.₄D₄	Direct product of S₃ and C₄.₄D₄	48		S3xC4.4D4	192,1232
C₄²⋊₂₀D₆	18^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:20D6	192,1233
D₁₂⋊₁₀D₄	3^rd semidirect product of D₁₂ and D₄ acting via D₄/C₄=C₂	48		D12:10D4	192,1235
C₄²⋊₂₂D₆	20^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:22D6	192,1237
C₄²⋊₂₃D₆	21^st semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:23D6	192,1238
C₄²⋊₂₄D₆	22^nd semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:24D6	192,1242
S₃×C₄²⋊₂C₂	Direct product of S₃ and C₄²⋊₂C₂	48		S3xC4^2:2C2	192,1262
C₄²⋊₂₅D₆	23^rd semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:25D6	192,1263
C₄²⋊₂₆D₆	24^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:26D6	192,1264
C₄²⋊₂₇D₆	25^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:27D6	192,1270
S₃×C₄⋊₁D₄	Direct product of S₃ and C₄⋊₁D₄	48		S3xC4:1D4	192,1273
C₄²⋊₂₈D₆	26^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:28D6	192,1274
D₁₂⋊₁₁D₄	4^th semidirect product of D₁₂ and D₄ acting via D₄/C₄=C₂	48		D12:11D4	192,1276
C₄²⋊₃₀D₆	28^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48		C4^2:30D6	192,1279
C₂×S₃×M₄(2)	Direct product of C₂, S₃ and M₄(2)	48		C2xS3xM4(2)	192,1302
M₄(2)⋊₂₆D₆	2^nd semidirect product of M₄(2) and D₆ acting through Inn(M₄(2))	48	4	M4(2):26D6	192,1304
C₂×C₈⋊D₆	Direct product of C₂ and C₈⋊D₆	48		C2xC8:D6	192,1305
C₂₄.₉C₂³	2^nd non-split extension by C₂₄ of C₂³ acting via C₂³/C₂=C₂²	48	4	C24.9C2^3	192,1307
S₃×C₈○D₄	Direct product of S₃ and C₈○D₄	48	4	S3xC8oD4	192,1308
M₄(2)⋊₂₈D₆	4^th semidirect product of M₄(2) and D₆ acting through Inn(M₄(2))	48	4	M4(2):28D6	192,1309
D₄.₁₁D₁₂	1^st non-split extension by D₄ of D₁₂ acting through Inn(D₄)	48	4	D4.11D12	192,1310
D₄.₁₂D₁₂	2^nd non-split extension by D₄ of D₁₂ acting through Inn(D₄)	48	4+	D4.12D12	192,1311
C₂×S₃×D₈	Direct product of C₂, S₃ and D₈	48		C2xS3xD8	192,1313
C₂×D₈⋊S₃	Direct product of C₂ and D₈⋊S₃	48		C2xD8:S3	192,1314
D₈⋊₁₃D₆	2^nd semidirect product of D₈ and D₆ acting through Inn(D₈)	48	4	D8:13D6	192,1316
C₂×S₃×SD₁₆	Direct product of C₂, S₃ and SD₁₆	48		C2xS3xSD16	192,1317
C₂×Q₈⋊₃D₆	Direct product of C₂ and Q₈⋊₃D₆	48		C2xQ8:3D6	192,1318
SD₁₆⋊₁₃D₆	2^nd semidirect product of SD₁₆ and D₆ acting through Inn(SD₁₆)	48	4	SD16:13D6	192,1321
S₃×C₄○D₈	Direct product of S₃ and C₄○D₈	48	4	S3xC4oD8	192,1326
SD₁₆⋊D₆	3^rd semidirect product of SD₁₆ and D₆ acting via D₆/C₆=C₂	48	4	SD16:D6	192,1327
D₈⋊₁₅D₆	4^th semidirect product of D₈ and D₆ acting through Inn(D₈)	48	4+	D8:15D6	192,1328
D₈⋊₁₁D₆	5^th semidirect product of D₈ and D₆ acting via D₆/C₆=C₂	48	4	D8:11D6	192,1329
D₈⋊₄D₆	4^th semidirect product of D₈ and D₆ acting via D₆/S₃=C₂	48	8-	D8:4D6	192,1332
D₈⋊₅D₆	5^th semidirect product of D₈ and D₆ acting via D₆/S₃=C₂	48	8+	D8:5D6	192,1333
D₈⋊₆D₆	6^th semidirect product of D₈ and D₆ acting via D₆/S₃=C₂	48	8-	D8:6D6	192,1334
S₃×C₈.C₂²	Direct product of S₃ and C₈.C₂²	48	8-	S3xC8.C2^2	192,1335
D₂₄⋊C₂²	3^rd semidirect product of D₂₄ and C₂² acting faithfully	48	8+	D24:C2^2	192,1336
C₂₄.C₂³	6^th non-split extension by C₂₄ of C₂³ acting faithfully	48	8+	C24.C2^3	192,1337
C₂⁴.₈₃D₆	12^nd non-split extension by C₂⁴ of D₆ acting via D₆/C₆=C₂	48		C2^4.83D6	192,1350
C₂×D₁₂⋊₆C₂²	Direct product of C₂ and D₁₂⋊₆C₂²	48		C2xD12:6C2^2	192,1352
C₂⁴.₄₉D₆	38^th non-split extension by C₂⁴ of D₆ acting via D₆/C₃=C₂²	48		C2^4.49D6	192,1357
C₂×C₂³⋊₂D₆	Direct product of C₂ and C₂³⋊₂D₆	48		C2xC2^3:2D6	192,1358
D₄×C₃⋊D₄	Direct product of D₄ and C₃⋊D₄	48		D4xC3:D4	192,1360
C₂⁴⋊₁₂D₆	7^th semidirect product of C₂⁴ and D₆ acting via D₆/C₃=C₂²	48		C2^4:12D6	192,1363
C₂⁴.₅₂D₆	41^st non-split extension by C₂⁴ of D₆ acting via D₆/C₃=C₂²	48		C2^4.52D6	192,1364
C₂⁴.₅₃D₆	42^nd non-split extension by C₂⁴ of D₆ acting via D₆/C₃=C₂²	48		C2^4.53D6	192,1365
C₁₂.₇₆C₂⁴	23^rd non-split extension by C₁₂ of C₂⁴ acting via C₂⁴/C₂³=C₂	48	4	C12.76C2^4	192,1378
C₂×D₄⋊D₆	Direct product of C₂ and D₄⋊D₆	48		C2xD4:D6	192,1379
C₁₂.C₂⁴	35^th non-split extension by C₁₂ of C₂⁴ acting via C₂⁴/C₂²=C₂²	48	4	C12.C2^4	192,1381
(C₂×D₄)⋊₄₃D₆	11^st semidirect product of C₂×D₄ and D₆ acting via D₆/C₆=C₂	48		(C2xD4):43D6	192,1387
C₆.₁₄₅2₊¹⁺⁴	54^th non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₄○D₄=C₂	48		C6.145ES+(2,2)	192,1388
C₆.₁₄₆2₊¹⁺⁴	55^th non-split extension by C₆ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₄○D₄=C₂	48		C6.146ES+(2,2)	192,1389
D₁₂.₃₂C₂³	13^rd non-split extension by D₁₂ of C₂³ acting via C₂³/C₂²=C₂	48	8+	D12.32C2^3	192,1394
D₁₂.₃₃C₂³	14^th non-split extension by D₁₂ of C₂³ acting via C₂³/C₂²=C₂	48	8-	D12.33C2^3	192,1395
D₁₂.₃₄C₂³	15^th non-split extension by D₁₂ of C₂³ acting via C₂³/C₂²=C₂	48	8+	D12.34C2^3	192,1396
C₂×C₂⁴⋊₄S₃	Direct product of C₂ and C₂⁴⋊₄S₃	48		C2xC2^4:4S3	192,1399
C₃×C₂².₁₁C₂⁴	Direct product of C₃ and C₂².₁₁C₂⁴	48		C3xC2^2.11C2^4	192,1407
C₆×C₂²≀C₂	Direct product of C₆ and C₂²≀C₂	48		C6xC2^2wrC2	192,1410
C₃×C₂².₁₉C₂⁴	Direct product of C₃ and C₂².₁₉C₂⁴	48		C3xC2^2.19C2^4	192,1414
C₃×C₂³⋊₃D₄	Direct product of C₃ and C₂³⋊₃D₄	48		C3xC2^3:3D4	192,1423
C₃×C₂².₂₉C₂⁴	Direct product of C₃ and C₂².₂₉C₂⁴	48		C3xC2^2.29C2^4	192,1424
C₃×C₂².₃₂C₂⁴	Direct product of C₃ and C₂².₃₂C₂⁴	48		C3xC2^2.32C2^4	192,1427
C₃×C₂³⋊₂Q₈	Direct product of C₃ and C₂³⋊₂Q₈	48		C3xC2^3:2Q8	192,1432
C₃×D₄²	Direct product of C₃, D₄ and D₄	48		C3xD4^2	192,1434
C₃×D₄⋊₅D₄	Direct product of C₃ and D₄⋊₅D₄	48		C3xD4:5D4	192,1435
C₃×C₂².₄₅C₂⁴	Direct product of C₃ and C₂².₄₅C₂⁴	48		C3xC2^2.45C2^4	192,1440
C₃×C₂².₅₄C₂⁴	Direct product of C₃ and C₂².₅₄C₂⁴	48		C3xC2^2.54C2^4	192,1449
C₃×C₂⁴⋊C₂²	Direct product of C₃ and C₂⁴⋊C₂²	48		C3xC2^4:C2^2	192,1450
C₃×Q₈○M₄(2)	Direct product of C₃ and Q₈○M₄(2)	48	4	C3xQ8oM4(2)	192,1457
C₆×C₈⋊C₂²	Direct product of C₆ and C₈⋊C₂²	48		C6xC8:C2^2	192,1462
C₃×D₈⋊C₂²	Direct product of C₃ and D₈⋊C₂²	48	4	C3xD8:C2^2	192,1464
C₃×D₄○D₈	Direct product of C₃ and D₄○D₈	48	4	C3xD4oD8	192,1465
C₃×D₄○SD₁₆	Direct product of C₃ and D₄○SD₁₆	48	4	C3xD4oSD16	192,1466
C₂×A₄⋊Q₈	Direct product of C₂ and A₄⋊Q₈	48		C2xA4:Q8	192,1468
C₂²×A₄⋊C₄	Direct product of C₂² and A₄⋊C₄	48		C2^2xA4:C4	192,1487
Q₈.₁S₄	1^st non-split extension by Q₈ of S₄ acting via S₄/C₂²=S₃	48	6-	Q8.1S4	192,1489
A₄×C₂²×C₄	Direct product of C₂²×C₄ and A₄	48		A4xC2^2xC4	192,1496
C₂×Q₈×A₄	Direct product of C₂, Q₈ and A₄	48		C2xQ8xA4	192,1499
C₂×Q₈.A₄	Direct product of C₂ and Q₈.A₄	48		C2xQ8.A4	192,1502
C₂×Q₈⋊A₄	Direct product of C₂ and Q₈⋊A₄	48		C2xQ8:A4	192,1506
C₂²×S₃×D₄	Direct product of C₂², S₃ and D₄	48		C2^2xS3xD4	192,1514
C₂×D₄⋊₆D₆	Direct product of C₂ and D₄⋊₆D₆	48		C2xD4:6D6	192,1516
C₂×S₃×C₄○D₄	Direct product of C₂, S₃ and C₄○D₄	48		C2xS3xC4oD4	192,1520
C₂×D₄○D₁₂	Direct product of C₂ and D₄○D₁₂	48		C2xD4oD12	192,1521
C₆.C₂⁵	14^th non-split extension by C₆ of C₂⁵ acting via C₂⁵/C₂⁴=C₂	48	4	C6.C2^5	192,1523
D₆.C₂⁴	9^th non-split extension by D₆ of C₂⁴ acting via C₂⁴/C₂³=C₂	48	8-	D6.C2^4	192,1525
S₃×2_-¹⁺⁴	Direct product of S₃ and 2_-¹⁺⁴	48	8-	S3xES-(2,2)	192,1526
D₁₂.₃₉C₂³	20^th non-split extension by D₁₂ of C₂³ acting via C₂³/C₂²=C₂	48	8+	D12.39C2^3	192,1527
C₆×2₊¹⁺⁴	Direct product of C₆ and 2₊¹⁺⁴	48		C6xES+(2,2)	192,1534
C₃×C₂.C₂⁵	Direct product of C₃ and C₂.C₂⁵	48	4	C3xC2.C2^5	192,1536
A₄×C₂⁴	Direct product of C₂⁴ and A₄	48		A4xC2^4	192,1539

Groups of order 240

		d	ρ	Label	ID
CSU₂(𝔽₅)	Conformal special unitary group on 𝔽₅²; = C₂ .₂ S₅	48	4-	CSU(2,5)	240,89
C₂×SL₂(𝔽₅)	Direct product of C₂ and SL₂(𝔽₅)	48		C2xSL(2,5)	240,94

Groups of order 288

		d	ρ	Label	ID
C₂₄.₆₀D₆	13^rd non-split extension by C₂₄ of D₆ acting via D₆/S₃=C₂	48	4	C24.60D6	288,190
C₂₄.₆₂D₆	15^th non-split extension by C₂₄ of D₆ acting via D₆/S₃=C₂	48	4	C24.62D6	288,192
C₃⋊D₄₈	The semidirect product of C₃ and D₄₈ acting via D₄₈/D₂₄=C₂	48	4+	C3:D48	288,194
C₂₄.₄₉D₆	2^nd non-split extension by C₂₄ of D₆ acting via D₆/S₃=C₂	48	4+	C24.49D6	288,197
C₁₂.₇₈D₁₂	9^th non-split extension by C₁₂ of D₁₂ acting via D₁₂/D₆=C₂	48		C12.78D12	288,205
C₁₂.D₁₂	13^rd non-split extension by C₁₂ of D₁₂ acting via D₁₂/C₆=C₂²	48	4	C12.D12	288,206
C₁₂.₁₄D₁₂	14^th non-split extension by C₁₂ of D₁₂ acting via D₁₂/C₆=C₂²	48	4	C12.14D12	288,208
C₁₂.₇₁D₁₂	2^nd non-split extension by C₁₂ of D₁₂ acting via D₁₂/D₆=C₂	48	4-	C12.71D12	288,209
C₆.₁₇D₂₄	6^th non-split extension by C₆ of D₂₄ acting via D₂₄/D₁₂=C₂	48		C6.17D24	288,212
D₁₂⋊₂Dic₃	2^nd semidirect product of D₁₂ and Dic₃ acting via Dic₃/C₆=C₂	48	4	D12:2Dic3	288,217
C₁₂.₈₀D₁₂	11^st non-split extension by C₁₂ of D₁₂ acting via D₁₂/D₆=C₂	48	4	C12.80D12	288,218
C₁₂.₈₂D₁₂	13^rd non-split extension by C₁₂ of D₁₂ acting via D₁₂/D₆=C₂	48	4	C12.82D12	288,225
C₆².₅Q₈	2^nd non-split extension by C₆² of Q₈ acting via Q₈/C₂=C₂²	48	4	C6^2.5Q8	288,226
C₃×C₁₂.C₈	Direct product of C₃ and C₁₂.C₈	48	2	C3xC12.C8	288,246
C₃×C₂₄.C₄	Direct product of C₃ and C₂₄.C₄	48	2	C3xC24.C4	288,253
C₃×C₁₂.₅₃D₄	Direct product of C₃ and C₁₂.₅₃D₄	48	4	C3xC12.53D4	288,256
C₃×C₁₂.₄₆D₄	Direct product of C₃ and C₁₂.₄₆D₄	48	4	C3xC12.46D4	288,257
C₃×C₁₂.₄₇D₄	Direct product of C₃ and C₁₂.₄₇D₄	48	4	C3xC12.47D4	288,258
C₃×D₁₂⋊C₄	Direct product of C₃ and D₁₂⋊C₄	48	4	C3xD12:C4	288,259
C₃×C₃⋊D₁₆	Direct product of C₃ and C₃⋊D₁₆	48	4	C3xC3:D16	288,260
C₃×D₈.S₃	Direct product of C₃ and D₈.S₃	48	4	C3xD8.S3	288,261
C₃×C₁₂.₅₅D₄	Direct product of C₃ and C₁₂.₅₅D₄	48		C3xC12.55D4	288,264
C₃×D₄⋊Dic₃	Direct product of C₃ and D₄⋊Dic₃	48		C3xD4:Dic3	288,266
C₃×C₁₂.₁₀D₄	Direct product of C₃ and C₁₂.₁₀D₄	48	4	C3xC12.10D4	288,270
C₃×Q₈⋊₃Dic₃	Direct product of C₃ and Q₈⋊₃Dic₃	48	4	C3xQ8:3Dic3	288,271
(C₃×C₁₂).D₄	2^nd non-split extension by C₃×C₁₂ of D₄ acting faithfully	48	4	(C3xC12).D4	288,376
C₃⋊S₃.₂Q₁₆	1^st non-split extension by C₃⋊S₃ of Q₁₆ acting via Q₁₆/C₄=C₂²	48	4	C3:S3.2Q16	288,378
C₃²⋊C₄≀C₂	The semidirect product of C₃² and C₄≀C₂ acting via C₄≀C₂/C₄=D₄	48	4	C3^2:C4wrC2	288,379
C₃²⋊C₄⋊C₈	2^nd semidirect product of C₃²⋊C₄ and C₈ acting via C₈/C₄=C₂	48	4	C3^2:C4:C8	288,380
C₄.₁₉S₃≀C₂	4^th central extension by C₄ of S₃≀C₂	48	4	C4.19S3wrC2	288,381
C₃²⋊D₁₆	The semidirect product of C₃² and D₁₆ acting via D₁₆/C₄=D₄	48	8+	C3^2:D16	288,382
C₃²⋊SD₃₂	The semidirect product of C₃² and SD₃₂ acting via SD₃₂/C₄=D₄	48	8+	C3^2:SD32	288,383
C₆².D₄	1^st non-split extension by C₆² of D₄ acting faithfully	48		C6^2.D4	288,385
C₆².₃D₄	3^rd non-split extension by C₆² of D₄ acting faithfully	48		C6^2.3D4	288,387
C₄.₄PSU₃(𝔽₂)	The central extension by C₄ of PSU₃(𝔽₂)	48	8	C4.4PSU(3,2)	288,392
C₄.PSU₃(𝔽₂)	1^st non-split extension by C₄ of PSU₃(𝔽₂) acting via PSU₃(𝔽₂)/C₃²⋊C₄=C₂	48	8	C4.PSU(3,2)	288,393
C₄.₂PSU₃(𝔽₂)	2^nd non-split extension by C₄ of PSU₃(𝔽₂) acting via PSU₃(𝔽₂)/C₃²⋊C₄=C₂	48	8	C4.2PSU(3,2)	288,394
C₆².Q₈	1^st non-split extension by C₆² of Q₈ acting faithfully	48		C6^2.Q8	288,395
C₆².₂Q₈	2^nd non-split extension by C₆² of Q₈ acting faithfully	48	8-	C6^2.2Q8	288,396
C₄²⋊C₃⋊S₃	1^st semidirect product of C₄²⋊C₃ and S₃ acting via S₃/C₃=C₂	48	6	C4^2:C3:S3	288,406
C₃⋊S₃⋊₃C₁₆	2^nd semidirect product of C₃⋊S₃ and C₁₆ acting via C₁₆/C₈=C₂	48	4	C3:S3:3C16	288,412
C₃²⋊₃M₅(2)	The semidirect product of C₃² and M₅(2) acting via M₅(2)/C₈=C₄	48	4	C3^2:3M5(2)	288,413
C₈×C₃²⋊C₄	Direct product of C₈ and C₃²⋊C₄	48	4	C8xC3^2:C4	288,414
(C₃×C₂₄)⋊C₄	2^nd semidirect product of C₃×C₂₄ and C₄ acting faithfully	48	4	(C3xC24):C4	288,415
C₈⋊(C₃²⋊C₄)	2^nd semidirect product of C₈ and C₃²⋊C₄ acting via C₃²⋊C₄/C₃⋊S₃=C₂	48	4	C8:(C3^2:C4)	288,416
C₃⋊S₃.₄D₈	The non-split extension by C₃⋊S₃ of D₈ acting via D₈/C₈=C₂	48	4	C3:S3.4D8	288,417
(C₃×C₂₄).C₄	4^th non-split extension by C₃×C₂₄ of C₄ acting faithfully	48	4	(C3xC24).C4	288,418
C₈.(C₃²⋊C₄)	1^st non-split extension by C₈ of C₃²⋊C₄ acting via C₃²⋊C₄/C₃⋊S₃=C₂	48	4	C8.(C3^2:C4)	288,419
C₆².₄C₈	2^nd non-split extension by C₆² of C₈ acting via C₈/C₂=C₄	48	4	C6^2.4C8	288,421
C₆².₆(C₂×C₄)	5^th non-split extension by C₆² of C₂×C₄ acting via C₂×C₄/C₂=C₄	48		C6^2.6(C2xC4)	288,426
C₃⋊Dic₃.D₄	9^th non-split extension by C₃⋊Dic₃ of D₄ acting via D₄/C₂=C₂²	48	4-	C3:Dic3.D4	288,428
(C₆×C₁₂)⋊₂C₄	2^nd semidirect product of C₆×C₁₂ and C₄ acting faithfully	48		(C6xC12):2C4	288,429
C₃²⋊₆C₄≀C₂	The semidirect product of C₃² and C₄≀C₂ acting via C₄≀C₂/D₄=C₄	48	8-	C3^2:6C4wrC2	288,431
C₃⋊S₃.₅Q₁₆	The non-split extension by C₃⋊S₃ of Q₁₆ acting via Q₁₆/Q₈=C₂	48	8-	C3:S3.5Q16	288,432
C₃²⋊₇C₄≀C₂	The semidirect product of C₃² and C₄≀C₂ acting via C₄≀C₂/Q₈=C₄	48	8+	C3^2:7C4wrC2	288,433
C₆²⋊₃C₈	1^st semidirect product of C₆² and C₈ acting via C₈/C₂=C₄	48		C6^2:3C8	288,435
S₃²×C₈	Direct product of C₈, S₃ and S₃	48	4	S3^2xC8	288,437
S₃×C₈⋊S₃	Direct product of S₃ and C₈⋊S₃	48	4	S3xC8:S3	288,438
C₂₄⋊D₆	14^th semidirect product of C₂₄ and D₆ acting via D₆/C₃=C₂²	48	4	C24:D6	288,439
S₃×C₂₄⋊C₂	Direct product of S₃ and C₂₄⋊C₂	48	4	S3xC24:C2	288,440
S₃×D₂₄	Direct product of S₃ and D₂₄	48	4+	S3xD24	288,441
C₂₄⋊₁D₆	1^st semidirect product of C₂₄ and D₆ acting via D₆/C₃=C₂²	48	4+	C24:1D6	288,442
D₂₄⋊S₃	2^nd semidirect product of D₂₄ and S₃ acting via S₃/C₃=C₂	48	4	D24:S3	288,443
C₂₄⋊₉D₆	9^th semidirect product of C₂₄ and D₆ acting via D₆/C₃=C₂²	48	4	C24:9D6	288,444
C₂₄⋊₄D₆	4^th semidirect product of C₂₄ and D₆ acting via D₆/C₃=C₂²	48	4	C24:4D6	288,445
C₂₄⋊₆D₆	6^th semidirect product of C₂₄ and D₆ acting via D₆/C₃=C₂²	48	4	C24:6D6	288,446
Dic₁₂⋊S₃	2^nd semidirect product of Dic₁₂ and S₃ acting via S₃/C₃=C₂	48	4	Dic12:S3	288,449
C₂₄.₂₃D₆	23^rd non-split extension by C₂₄ of D₆ acting via D₆/C₃=C₂²	48	4	C24.23D6	288,450
C₂₄.₆₃D₆	16^th non-split extension by C₂₄ of D₆ acting via D₆/S₃=C₂	48	4	C24.63D6	288,451
C₂₄.₆₄D₆	17^th non-split extension by C₂₄ of D₆ acting via D₆/S₃=C₂	48	4	C24.64D6	288,452
C₂₄.D₆	46^th non-split extension by C₂₄ of D₆ acting via D₆/C₃=C₂²	48	4	C24.D6	288,453
D₆.₁D₁₂	1^st non-split extension by D₆ of D₁₂ acting via D₁₂/C₁₂=C₂	48	4	D6.1D12	288,454
D₆.₃D₁₂	3^rd non-split extension by D₆ of D₁₂ acting via D₁₂/C₁₂=C₂	48	4+	D6.3D12	288,456
D₁₂.₂D₆	2^nd non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	4	D12.2D6	288,457
D₂₄⋊₅S₃	5^th semidirect product of D₂₄ and S₃ acting via S₃/C₃=C₂	48	4	D24:5S3	288,458
D₁₂.₄D₆	4^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	4	D12.4D6	288,459
S₃×C₄.Dic₃	Direct product of S₃ and C₄.Dic₃	48	4	S3xC4.Dic3	288,461
D₁₂.₂Dic₃	The non-split extension by D₁₂ of Dic₃ acting through Inn(D₁₂)	48	4	D12.2Dic3	288,462
D₁₂.Dic₃	The non-split extension by D₁₂ of Dic₃ acting via Dic₃/C₆=C₂	48	4	D12.Dic3	288,463
C₂×C₁₂.₂₉D₆	Direct product of C₂ and C₁₂.₂₉D₆	48		C2xC12.29D6	288,464
C₃⋊C₈.₂₂D₆	11^st non-split extension by C₃⋊C₈ of D₆ acting via D₆/S₃=C₂	48	4	C3:C8.22D6	288,465
C₂×C₁₂.₃₁D₆	Direct product of C₂ and C₁₂.₃₁D₆	48		C2xC12.31D6	288,468
D₁₂.₃₀D₆	5^th non-split extension by D₁₂ of D₆ acting via D₆/C₆=C₂	48	4	D12.30D6	288,470
D₁₂⋊₂₀D₆	4^th semidirect product of D₁₂ and D₆ acting via D₆/C₆=C₂	48	4	D12:20D6	288,471
C₂×C₃⋊D₂₄	Direct product of C₂ and C₃⋊D₂₄	48		C2xC3:D24	288,472
D₁₂.₃₂D₆	7^th non-split extension by D₁₂ of D₆ acting via D₆/C₆=C₂	48	4	D12.32D6	288,475
D₁₂.₂₇D₆	2^nd non-split extension by D₁₂ of D₆ acting via D₆/C₆=C₂	48	4	D12.27D6	288,477
D₁₂.₂₈D₆	3^rd non-split extension by D₁₂ of D₆ acting via D₆/C₆=C₂	48	4	D12.28D6	288,478
D₁₂.₂₉D₆	4^th non-split extension by D₁₂ of D₆ acting via D₆/C₆=C₂	48	4-	D12.29D6	288,479
C₂×C₃²⋊₅SD₁₆	Direct product of C₂ and C₃²⋊₅SD₁₆	48		C2xC3^2:5SD16	288,480
Dic₆.₂₉D₆	3^rd non-split extension by Dic₆ of D₆ acting via D₆/C₆=C₂	48	4	Dic6.29D6	288,481
C₆².₆C₂³	1^st non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.6C2^3	288,484
C₆².₁₈C₂³	13^rd non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.18C2^3	288,496
C₆².₁₉C₂³	14^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.19C2^3	288,497
C₆².₂₀C₂³	15^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.20C2^3	288,498
Dic₃.D₁₂	4^th non-split extension by Dic₃ of D₁₂ acting via D₁₂/C₁₂=C₂	48		Dic3.D12	288,500
C₆².₂₃C₂³	18^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.23C2^3	288,501
C₆².₂₄C₂³	19^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.24C2^3	288,502
C₁₂.₂₈D₁₂	28^th non-split extension by C₁₂ of D₁₂ acting via D₁₂/C₆=C₂²	48		C12.28D12	288,512
C₆².₃₅C₂³	30^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.35C2^3	288,513
C₆².₃₈C₂³	33^rd non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.38C2^3	288,516
C₁₂.₃₀D₁₂	30^th non-split extension by C₁₂ of D₁₂ acting via D₁₂/C₆=C₂²	48		C12.30D12	288,519
C₆².₄₄C₂³	39^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.44C2^3	288,522
Dic₃⋊₄D₁₂	1^st semidirect product of Dic₃ and D₁₂ acting through Inn(Dic₃)	48		Dic3:4D12	288,528
C₆².₅₁C₂³	46^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.51C2^3	288,529
C₄×C₆.D₆	Direct product of C₄ and C₆.D₆	48		C4xC6.D6	288,530
C₆².₅₃C₂³	48^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.53C2^3	288,531
Dic₃⋊D₁₂	1^st semidirect product of Dic₃ and D₁₂ acting via D₁₂/D₆=C₂	48		Dic3:D12	288,534
C₆².₅₈C₂³	53^rd non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.58C2^3	288,536
D₆.D₁₂	5^th non-split extension by D₆ of D₁₂ acting via D₁₂/D₆=C₂	48		D6.D12	288,538
Dic₃⋊₅D₁₂	2^nd semidirect product of Dic₃ and D₁₂ acting through Inn(Dic₃)	48		Dic3:5D12	288,542
C₆².₆₅C₂³	60^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.65C2^3	288,543
C₆².₆₇C₂³	62^nd non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.67C2^3	288,545
C₆².₇₀C₂³	65^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.70C2^3	288,548
C₄×C₃⋊D₁₂	Direct product of C₄ and C₃⋊D₁₂	48		C4xC3:D12	288,551
C₆².₇₄C₂³	69^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.74C2^3	288,552
D₆⋊D₁₂	1^st semidirect product of D₆ and D₁₂ acting via D₁₂/C₁₂=C₂	48		D6:D12	288,554
C₆².₇₇C₂³	72^nd non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.77C2^3	288,555
C₁₂⋊₇D₁₂	1^st semidirect product of C₁₂ and D₁₂ acting via D₁₂/D₆=C₂	48		C12:7D12	288,557
Dic₃⋊₃D₁₂	2^nd semidirect product of Dic₃ and D₁₂ acting via D₁₂/D₆=C₂	48		Dic3:3D12	288,558
C₁₂⋊D₁₂	1^st semidirect product of C₁₂ and D₁₂ acting via D₁₂/C₆=C₂²	48		C12:D12	288,559
C₆².₈₂C₂³	77^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.82C2^3	288,560
C₁₂⋊₂D₁₂	2^nd semidirect product of C₁₂ and D₁₂ acting via D₁₂/C₆=C₂²	48		C12:2D12	288,564
S₃×D₆⋊C₄	Direct product of S₃ and D₆⋊C₄	48		S3xD6:C4	288,568
C₆².₉₁C₂³	86^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.91C2^3	288,569
D₆⋊₄D₁₂	1^st semidirect product of D₆ and D₁₂ acting via D₁₂/D₆=C₂	48		D6:4D12	288,570
D₆⋊₅D₁₂	2^nd semidirect product of D₆ and D₁₂ acting via D₁₂/D₆=C₂	48		D6:5D12	288,571
S₃×D₄⋊S₃	Direct product of S₃ and D₄⋊S₃	48	8+	S3xD4:S3	288,572
Dic₆⋊₃D₆	3^rd semidirect product of Dic₆ and D₆ acting via D₆/C₃=C₂²	48	8+	Dic6:3D6	288,573
D₁₂.D₆	5^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8-	D12.D6	288,575
S₃×D₄.S₃	Direct product of S₃ and D₄.S₃	48	8-	S3xD4.S3	288,576
Dic₆.₁₉D₆	6^th non-split extension by Dic₆ of D₆ acting via D₆/S₃=C₂	48	8-	Dic6.19D6	288,577
Dic₆.D₆	5^th non-split extension by Dic₆ of D₆ acting via D₆/C₃=C₂²	48	8-	Dic6.D6	288,579
D₁₂⋊₉D₆	3^rd semidirect product of D₁₂ and D₆ acting via D₆/S₃=C₂	48	8-	D12:9D6	288,580
D₁₂.₂₂D₆	7^th non-split extension by D₁₂ of D₆ acting via D₆/S₃=C₂	48	8-	D12.22D6	288,581
D₁₂.₇D₆	7^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8+	D12.7D6	288,582
Dic₆.₂₀D₆	7^th non-split extension by Dic₆ of D₆ acting via D₆/S₃=C₂	48	8+	Dic6.20D6	288,583
D₁₂.₈D₆	8^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8-	D12.8D6	288,584
S₃×Q₈⋊₂S₃	Direct product of S₃ and Q₈⋊₂S₃	48	8+	S3xQ8:2S3	288,586
D₁₂⋊₆D₆	6^th semidirect product of D₁₂ and D₆ acting via D₆/C₃=C₂²	48	8+	D12:6D6	288,587
D₁₂.₉D₆	9^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8-	D12.9D6	288,588
D₁₂.₁₀D₆	10^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8+	D12.10D6	288,589
Dic₆.₉D₆	9^th non-split extension by Dic₆ of D₆ acting via D₆/C₃=C₂²	48	8-	Dic6.9D6	288,592
Dic₆.₁₀D₆	10^th non-split extension by Dic₆ of D₆ acting via D₆/C₃=C₂²	48	8+	Dic6.10D6	288,593
Dic₆.₂₂D₆	9^th non-split extension by Dic₆ of D₆ acting via D₆/S₃=C₂	48	8+	Dic6.22D6	288,596
D₁₂.₁₃D₆	13^rd non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8+	D12.13D6	288,597
D₁₂.₁₄D₆	14^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8+	D12.14D6	288,598
D₁₂.₁₅D₆	15^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8-	D12.15D6	288,599
C₆².₉₄C₂³	89^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.94C2^3	288,600
C₆².₉₅C₂³	90^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.95C2^3	288,601
C₆².₉₇C₂³	92^nd non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.97C2^3	288,603
C₆².₉₈C₂³	93^rd non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.98C2^3	288,604
C₆².₉₉C₂³	94^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.99C2^3	288,605
C₆².₁₀₀C₂³	95^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.100C2^3	288,606
C₆².₁₀₁C₂³	96^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.101C2^3	288,607
C₆².₅₆D₄	40^th non-split extension by C₆² of D₄ acting via D₄/C₂=C₂²	48		C6^2.56D4	288,609
C₆².₅₇D₄	41^st non-split extension by C₆² of D₄ acting via D₄/C₂=C₂²	48		C6^2.57D4	288,610
C₂×C₆.D₁₂	Direct product of C₂ and C₆.D₁₂	48		C2xC6.D12	288,611
C₆²⋊₃Q₈	1^st semidirect product of C₆² and Q₈ acting via Q₈/C₂=C₂²	48		C6^2:3Q8	288,612
C₆².₆₀D₄	44^th non-split extension by C₆² of D₄ acting via D₄/C₂=C₂²	48		C6^2.60D4	288,614
S₃×C₆.D₄	Direct product of S₃ and C₆.D₄	48		S3xC6.D4	288,616
C₆².₁₁₁C₂³	106^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.111C2^3	288,617
C₆².₁₁₂C₂³	107^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.112C2^3	288,618
C₆².₁₁₃C₂³	108^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.113C2^3	288,619
Dic₃×C₃⋊D₄	Direct product of Dic₃ and C₃⋊D₄	48		Dic3xC3:D4	288,620
C₆².₁₁₅C₂³	110^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.115C2^3	288,621
C₆².₁₁₇C₂³	112^nd non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.117C2^3	288,623
C₆²⋊₄D₄	1^st semidirect product of C₆² and D₄ acting via D₄/C₂=C₂²	48		C6^2:4D4	288,624
C₆²⋊₅D₄	2^nd semidirect product of C₆² and D₄ acting via D₄/C₂=C₂²	48		C6^2:5D4	288,625
C₆²⋊₆D₄	3^rd semidirect product of C₆² and D₄ acting via D₄/C₂=C₂²	48		C6^2:6D4	288,626
C₆².₁₂₁C₂³	116^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.121C2^3	288,627
C₆²⋊₇D₄	4^th semidirect product of C₆² and D₄ acting via D₄/C₂=C₂²	48		C6^2:7D4	288,628
C₆²⋊₄Q₈	2^nd semidirect product of C₆² and Q₈ acting via Q₈/C₂=C₂²	48		C6^2:4Q8	288,630
C₆².₁₂₅C₂³	120^th non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	48		C6^2.125C2^3	288,631
C₃×C₄²⋊C₆	Direct product of C₃ and C₄²⋊C₆	48	6	C3xC4^2:C6	288,635
C₃×C₂³.₁₆D₆	Direct product of C₃ and C₂³.₁₆D₆	48		C3xC2^3.16D6	288,648
C₃×Dic₃.D₄	Direct product of C₃ and Dic₃.D₄	48		C3xDic3.D4	288,649
C₃×C₂³.₈D₆	Direct product of C₃ and C₂³.₈D₆	48		C3xC2^3.8D6	288,650
C₃×S₃×C₂²⋊C₄	Direct product of C₃, S₃ and C₂²⋊C₄	48		C3xS3xC2^2:C4	288,651
C₃×Dic₃⋊₄D₄	Direct product of C₃ and Dic₃⋊₄D₄	48		C3xDic3:4D4	288,652
C₃×D₆⋊D₄	Direct product of C₃ and D₆⋊D₄	48		C3xD6:D4	288,653
C₃×C₂³.₉D₆	Direct product of C₃ and C₂³.₉D₆	48		C3xC2^3.9D6	288,654
C₃×Dic₃⋊D₄	Direct product of C₃ and Dic₃⋊D₄	48		C3xDic3:D4	288,655
C₃×C₂³.₁₁D₆	Direct product of C₃ and C₂³.₁₁D₆	48		C3xC2^3.11D6	288,656
C₃×C₂³.₂₁D₆	Direct product of C₃ and C₂³.₂₁D₆	48		C3xC2^3.21D6	288,657
C₃×C₈○D₁₂	Direct product of C₃ and C₈○D₁₂	48	2	C3xC8oD12	288,672
C₃×C₄○D₂₄	Direct product of C₃ and C₄○D₂₄	48	2	C3xC4oD24	288,675
C₃×S₃×M₄(2)	Direct product of C₃, S₃ and M₄(2)	48	4	C3xS3xM4(2)	288,677
C₃×D₁₂.C₄	Direct product of C₃ and D₁₂.C₄	48	4	C3xD12.C4	288,678
C₃×C₈⋊D₆	Direct product of C₃ and C₈⋊D₆	48	4	C3xC8:D6	288,679
C₃×C₈.D₆	Direct product of C₃ and C₈.D₆	48	4	C3xC8.D6	288,680
C₃×S₃×D₈	Direct product of C₃, S₃ and D₈	48	4	C3xS3xD8	288,681
C₃×D₈⋊S₃	Direct product of C₃ and D₈⋊S₃	48	4	C3xD8:S3	288,682
C₃×D₈⋊₃S₃	Direct product of C₃ and D₈⋊₃S₃	48	4	C3xD8:3S3	288,683
C₃×S₃×SD₁₆	Direct product of C₃, S₃ and SD₁₆	48	4	C3xS3xSD16	288,684
C₃×Q₈⋊₃D₆	Direct product of C₃ and Q₈⋊₃D₆	48	4	C3xQ8:3D6	288,685
C₃×D₄.D₆	Direct product of C₃ and D₄.D₆	48	4	C3xD4.D6	288,686
C₃×Q₈.₇D₆	Direct product of C₃ and Q₈.₇D₆	48	4	C3xQ8.7D6	288,687
C₆×C₄.Dic₃	Direct product of C₆ and C₄.Dic₃	48		C6xC4.Dic3	288,692
C₃×C₁₂.₄₈D₄	Direct product of C₃ and C₁₂.₄₈D₄	48		C3xC12.48D4	288,695
C₃×C₂³.₂₆D₆	Direct product of C₃ and C₂³.₂₆D₆	48		C3xC2^3.26D6	288,697
C₁₂×C₃⋊D₄	Direct product of C₁₂ and C₃⋊D₄	48		C12xC3:D4	288,699
C₃×C₂³.₂₈D₆	Direct product of C₃ and C₂³.₂₈D₆	48		C3xC2^3.28D6	288,700
C₃×C₁₂⋊₇D₄	Direct product of C₃ and C₁₂⋊₇D₄	48		C3xC12:7D4	288,701
C₆×D₄⋊S₃	Direct product of C₆ and D₄⋊S₃	48		C6xD4:S3	288,702
C₆×D₄.S₃	Direct product of C₆ and D₄.S₃	48		C6xD4.S3	288,704
C₃×D₄×Dic₃	Direct product of C₃, D₄ and Dic₃	48		C3xD4xDic3	288,705
C₃×C₂³.₂₃D₆	Direct product of C₃ and C₂³.₂₃D₆	48		C3xC2^3.23D6	288,706
C₃×C₂³.₁₂D₆	Direct product of C₃ and C₂³.₁₂D₆	48		C3xC2^3.12D6	288,707
C₃×C₂³⋊₂D₆	Direct product of C₃ and C₂³⋊₂D₆	48		C3xC2^3:2D6	288,708
C₃×D₆⋊₃D₄	Direct product of C₃ and D₆⋊₃D₄	48		C3xD6:3D4	288,709
C₃×C₂³.₁₄D₆	Direct product of C₃ and C₂³.₁₄D₆	48		C3xC2^3.14D6	288,710
C₃×C₁₂⋊₃D₄	Direct product of C₃ and C₁₂⋊₃D₄	48		C3xC12:3D4	288,711
C₃×Q₈.₁₁D₆	Direct product of C₃ and Q₈.₁₁D₆	48	4	C3xQ8.11D6	288,713
C₃×D₄.Dic₃	Direct product of C₃ and D₄.Dic₃	48	4	C3xD4.Dic3	288,719
C₃×D₄⋊D₆	Direct product of C₃ and D₄⋊D₆	48	4	C3xD4:D6	288,720
C₃×Q₈.₁₃D₆	Direct product of C₃ and Q₈.₁₃D₆	48	4	C3xQ8.13D6	288,721
C₃×Q₈.₁₄D₆	Direct product of C₃ and Q₈.₁₄D₆	48	4	C3xQ8.14D6	288,722
C₆×C₆.D₄	Direct product of C₆ and C₆.D₄	48		C6xC6.D4	288,723
Dic₃.₄S₄	1^st non-split extension by Dic₃ of S₄ acting through Inn(Dic₃)	48	4	Dic3.4S4	288,845
Dic₃.₅S₄	2^nd non-split extension by Dic₃ of S₄ acting through Inn(Dic₃)	48	4+	Dic3.5S4	288,846
GL₂(𝔽₃)⋊S₃	1^st semidirect product of GL₂(𝔽₃) and S₃ acting via S₃/C₃=C₂	48	4+	GL(2,3):S3	288,847
S₃×CSU₂(𝔽₃)	Direct product of S₃ and CSU₂(𝔽₃)	48	4-	S3xCSU(2,3)	288,848
D₆.S₄	1^st non-split extension by D₆ of S₄ acting via S₄/A₄=C₂	48	4-	D6.S4	288,849
D₆.₂S₄	2^nd non-split extension by D₆ of S₄ acting via S₄/A₄=C₂	48	4	D6.2S4	288,850
C₄.₃F₉	2^nd central extension by C₄ of F₉	48	8	C4.3F9	288,861
C₄.F₉	The non-split extension by C₄ of F₉ acting via F₉/C₃²⋊C₄=C₂	48	8	C4.F9	288,862
C₂².F₉	The non-split extension by C₂² of F₉ acting via F₉/C₃²⋊C₄=C₂	48	8-	C2^2.F9	288,866
C₃²⋊C₄⋊Q₈	1^st semidirect product of C₃²⋊C₄ and Q₈ acting via Q₈/C₄=C₂	48	8-	C3^2:C4:Q8	288,870
C₃²⋊D₈⋊₅C₂	The semidirect product of C₃²⋊D₈ and C₂ acting through Inn(C₃²⋊D₈)	48	4	C3^2:D8:5C2	288,871
C₃²⋊Q₁₆⋊C₂	1^st semidirect product of C₃²⋊Q₁₆ and C₂ acting faithfully	48	4	C3^2:Q16:C2	288,874
C₃⋊S₃⋊Q₁₆	The semidirect product of C₃⋊S₃ and Q₁₆ acting via Q₁₆/C₄=C₂²	48	8-	C3:S3:Q16	288,876
C₂×C₃⋊S₃.Q₈	Direct product of C₂ and C₃⋊S₃.Q₈	48		C2xC3:S3.Q8	288,882
C₂×C₃²⋊D₈	Direct product of C₂ and C₃²⋊D₈	48		C2xC3^2:D8	288,883
C₆².₁₃D₄	13^rd non-split extension by C₆² of D₄ acting faithfully	48	8-	C6^2.13D4	288,885
C₂×C₃²⋊₂SD₁₆	Direct product of C₂ and C₃²⋊₂SD₁₆	48		C2xC3^2:2SD16	288,886
C₆².₁₅D₄	15^th non-split extension by C₆² of D₄ acting faithfully	48	4-	C6^2.15D4	288,887
C₄.₃PSU₃(𝔽₂)	3^rd non-split extension by C₄ of PSU₃(𝔽₂) acting via PSU₃(𝔽₂)/C₃²⋊C₄=C₂	48	8	C4.3PSU(3,2)	288,891
C₂×C₂.PSU₃(𝔽₂)	Direct product of C₂ and C₂.PSU₃(𝔽₂)	48		C2xC2.PSU(3,2)	288,894
C₆×GL₂(𝔽₃)	Direct product of C₆ and GL₂(𝔽₃)	48		C6xGL(2,3)	288,900
C₃×Q₈.D₆	Direct product of C₃ and Q₈.D₆	48	4	C3xQ8.D6	288,901
C₃×C₄.₆S₄	Direct product of C₃ and C₄.₆S₄	48	2	C3xC4.6S4	288,903
C₃×C₄.₃S₄	Direct product of C₃ and C₄.₃S₄	48	4	C3xC4.3S4	288,904
C₂×C₆.₆S₄	Direct product of C₂ and C₆.₆S₄	48		C2xC6.6S4	288,911
SL₂(𝔽₃).D₆	2^nd non-split extension by SL₂(𝔽₃) of D₆ acting via D₆/C₆=C₂	48	4	SL(2,3).D6	288,912
C₁₂.₁₄S₄	14^th non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	48	4	C12.14S4	288,914
C₁₂.₇S₄	7^th non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	48	4+	C12.7S4	288,915
C₂×S₃×SL₂(𝔽₃)	Direct product of C₂, S₃ and SL₂(𝔽₃)	48		C2xS3xSL(2,3)	288,922
SL₂(𝔽₃).₁₁D₆	1^st non-split extension by SL₂(𝔽₃) of D₆ acting through Inn(SL₂(𝔽₃))	48	4	SL(2,3).11D6	288,923
S₃×C₄.A₄	Direct product of S₃ and C₄.A₄	48	4	S3xC4.A4	288,925
D₁₂.A₄	The non-split extension by D₁₂ of A₄ acting through Inn(D₁₂)	48	4-	D12.A4	288,926
C₂×C₃⋊S₃⋊₃C₈	Direct product of C₂ and C₃⋊S₃⋊₃C₈	48		C2xC3:S3:3C8	288,929
C₂×C₃²⋊M₄(2)	Direct product of C₂ and C₃²⋊M₄(2)	48		C2xC3^2:M4(2)	288,930
C₂×C₄×C₃²⋊C₄	Direct product of C₂×C₄ and C₃²⋊C₄	48		C2xC4xC3^2:C4	288,932
C₂×C₄⋊(C₃²⋊C₄)	Direct product of C₂ and C₄⋊(C₃²⋊C₄)	48		C2xC4:(C3^2:C4)	288,933
C₆².(C₂×C₄)	The non-split extension by C₆² of C₂×C₄ acting faithfully	48	8-	C6^2.(C2xC4)	288,935
C₁₂⋊S₃.C₄	The non-split extension by C₁₂⋊S₃ of C₄ acting faithfully	48	8+	C12:S3.C4	288,937
Q₈×C₃²⋊C₄	Direct product of Q₈ and C₃²⋊C₄	48	8-	Q8xC3^2:C4	288,938
C₂×C₆².C₄	Direct product of C₂ and C₆².C₄	48		C2xC6^2.C4	288,940
C₂×D₁₂⋊S₃	Direct product of C₂ and D₁₂⋊S₃	48		C2xD12:S3	288,944
D₁₂.₃₃D₆	8^th non-split extension by D₁₂ of D₆ acting via D₆/C₆=C₂	48	4	D12.33D6	288,945
D₁₂.₃₄D₆	The non-split extension by D₁₂ of D₆ acting through Inn(D₁₂)	48	4-	D12.34D6	288,946
C₂×Dic₃.D₆	Direct product of C₂ and Dic₃.D₆	48		C2xDic3.D6	288,947
C₂×D₆.D₆	Direct product of C₂ and D₆.D₆	48		C2xD6.D6	288,948
C₂×D₆.₆D₆	Direct product of C₂ and D₆.₆D₆	48		C2xD6.6D6	288,949
S₃²×C₂×C₄	Direct product of C₂×C₄, S₃ and S₃	48		S3^2xC2xC4	288,950
C₂×S₃×D₁₂	Direct product of C₂, S₃ and D₁₂	48		C2xS3xD12	288,951
C₂×D₆⋊D₆	Direct product of C₂ and D₆⋊D₆	48		C2xD6:D6	288,952
S₃×C₄○D₁₂	Direct product of S₃ and C₄○D₁₂	48	4	S3xC4oD12	288,953
D₁₂⋊₂₄D₆	8^th semidirect product of D₁₂ and D₆ acting via D₆/C₆=C₂	48	4	D12:24D6	288,955
Dic₆.₂₄D₆	11^st non-split extension by Dic₆ of D₆ acting via D₆/S₃=C₂	48	8-	Dic6.24D6	288,957
S₃×D₄⋊₂S₃	Direct product of S₃ and D₄⋊₂S₃	48	8-	S3xD4:2S3	288,959
D₁₂⋊₁₂D₆	6^th semidirect product of D₁₂ and D₆ acting via D₆/S₃=C₂	48	8-	D12:12D6	288,961
D₁₂.₂₅D₆	10^th non-split extension by D₁₂ of D₆ acting via D₆/S₃=C₂	48	8-	D12.25D6	288,963
Dic₆.₂₆D₆	13^rd non-split extension by Dic₆ of D₆ acting via D₆/S₃=C₂	48	8+	Dic6.26D6	288,964
S₃²×Q₈	Direct product of S₃, S₃ and Q₈	48	8-	S3^2xQ8	288,965
S₃×Q₈⋊₃S₃	Direct product of S₃ and Q₈⋊₃S₃	48	8+	S3xQ8:3S3	288,966
D₁₂⋊₁₅D₆	9^th semidirect product of D₁₂ and D₆ acting via D₆/S₃=C₂	48	8-	D12:15D6	288,967
D₁₂⋊₁₆D₆	10^th semidirect product of D₁₂ and D₆ acting via D₆/S₃=C₂	48	8+	D12:16D6	288,968
C₂×D₆.₃D₆	Direct product of C₂ and D₆.₃D₆	48		C2xD6.3D6	288,970
C₂×D₆.₄D₆	Direct product of C₂ and D₆.₄D₆	48		C2xD6.4D6	288,971
C₂²×C₆.D₆	Direct product of C₂² and C₆.D₆	48		C2^2xC6.D6	288,972
C₂²×C₃⋊D₁₂	Direct product of C₂² and C₃⋊D₁₂	48		C2^2xC3:D12	288,974
C₂×S₃×C₃⋊D₄	Direct product of C₂, S₃ and C₃⋊D₄	48		C2xS3xC3:D4	288,976
C₃×D₄.A₄	Direct product of C₃ and D₄.A₄	48	4	C3xD4.A4	288,985
C₆×C₄○D₁₂	Direct product of C₆ and C₄○D₁₂	48		C6xC4oD12	288,991
S₃×C₆×D₄	Direct product of C₆, S₃ and D₄	48		S3xC6xD4	288,992
C₆×D₄⋊₂S₃	Direct product of C₆ and D₄⋊₂S₃	48		C6xD4:2S3	288,993
C₃×Q₈.₁₅D₆	Direct product of C₃ and Q₈.₁₅D₆	48	4	C3xQ8.15D6	288,997
C₃×S₃×C₄○D₄	Direct product of C₃, S₃ and C₄○D₄	48	4	C3xS3xC4oD4	288,998
C₃×D₄○D₁₂	Direct product of C₃ and D₄○D₁₂	48	4	C3xD4oD12	288,999
C₃×Q₈○D₁₂	Direct product of C₃ and Q₈○D₁₂	48	4	C3xQ8oD12	288,1000
C₂×C₆×C₃⋊D₄	Direct product of C₂×C₆ and C₃⋊D₄	48		C2xC6xC3:D4	288,1002
C₂³×C₃²⋊C₄	Direct product of C₂³ and C₃²⋊C₄	48		C2^3xC3^2:C4	288,1039
S₃²×C₂³	Direct product of C₂³, S₃ and S₃	48		S3^2xC2^3	288,1040

Groups of order 432

		d	ρ	Label	ID
C₃×C₃²⋊₂C₁₆	Direct product of C₃ and C₃²⋊₂C₁₆	48	4	C3xC3^2:2C16	432,412
C₃³⋊₄C₁₆	2^nd semidirect product of C₃³ and C₁₆ acting via C₁₆/C₄=C₄	48	4	C3^3:4C16	432,413
C₃×S₃×C₃⋊C₈	Direct product of C₃, S₃ and C₃⋊C₈	48	4	C3xS3xC3:C8	432,414
C₃×C₁₂.₂₉D₆	Direct product of C₃ and C₁₂.₂₉D₆	48	4	C3xC12.29D6	432,415
C₃×D₆.Dic₃	Direct product of C₃ and D₆.Dic₃	48	4	C3xD6.Dic3	432,416
C₃×C₁₂.₃₁D₆	Direct product of C₃ and C₁₂.₃₁D₆	48	4	C3xC12.31D6	432,417
C₃×C₃²⋊₂D₈	Direct product of C₃ and C₃²⋊₂D₈	48	4	C3xC3^2:2D8	432,418
C₃×C₃⋊D₂₄	Direct product of C₃ and C₃⋊D₂₄	48	4	C3xC3:D24	432,419
C₃×Dic₆⋊S₃	Direct product of C₃ and Dic₆⋊S₃	48	4	C3xDic6:S3	432,420
C₃×D₁₂.S₃	Direct product of C₃ and D₁₂.S₃	48	4	C3xD12.S3	432,421
C₃×C₃²⋊₅SD₁₆	Direct product of C₃ and C₃²⋊₅SD₁₆	48	4	C3xC3^2:5SD16	432,422
C₃×C₃²⋊₂Q₁₆	Direct product of C₃ and C₃²⋊₂Q₁₆	48	4	C3xC3^2:2Q16	432,423
C₃×C₃²⋊₃Q₁₆	Direct product of C₃ and C₃²⋊₃Q₁₆	48	4	C3xC3^2:3Q16	432,424
C₃×Dic₃²	Direct product of C₃, Dic₃ and Dic₃	48		C3xDic3^2	432,425
C₃×D₆⋊Dic₃	Direct product of C₃ and D₆⋊Dic₃	48		C3xD6:Dic3	432,426
C₃×C₆.D₁₂	Direct product of C₃ and C₆.D₁₂	48		C3xC6.D12	432,427
C₃×Dic₃⋊Dic₃	Direct product of C₃ and Dic₃⋊Dic₃	48		C3xDic3:Dic3	432,428
C₃×C₆².C₂²	Direct product of C₃ and C₆².C₂²	48		C3xC6^2.C2^2	432,429
C₁₂.₉₃S₃²	13^rd non-split extension by C₁₂ of S₃² acting via S₃²/C₃⋊S₃=C₂	48	4	C12.93S3^2	432,455
C₃³⋊₁₀M₄(2)	6^th semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₄=C₂²	48	4	C3^3:10M4(2)	432,456
C₃³⋊₉D₈	6^th semidirect product of C₃³ and D₈ acting via D₈/C₄=C₂²	48	4	C3^3:9D8	432,457
C₃³⋊₁₈SD₁₆	10^th semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₄=C₂²	48	4	C3^3:18SD16	432,458
C₃³⋊₉Q₁₆	6^th semidirect product of C₃³ and Q₁₆ acting via Q₁₆/C₄=C₂²	48	4	C3^3:9Q16	432,459
C₃³⋊₆C₄²	3^rd semidirect product of C₃³ and C₄² acting via C₄²/C₂²=C₂²	48		C3^3:6C4^2	432,460
C₆².₈₄D₆	32^nd non-split extension by C₆² of D₆ acting via D₆/C₃=C₂²	48		C6^2.84D6	432,461
C₆².₈₅D₆	33^rd non-split extension by C₆² of D₆ acting via D₆/C₃=C₂²	48		C6^2.85D6	432,462
C₃×C₂.F₉	Direct product of C₃ and C₂.F₉	48	8	C3xC2.F9	432,565
C₆.F₉	3^rd non-split extension by C₆ of F₉ acting via F₉/C₃²⋊C₄=C₂	48	8	C6.F9	432,566
Dic₃×C₃²⋊C₄	Direct product of Dic₃ and C₃²⋊C₄	48	8-	Dic3xC3^2:C4	432,567
C₃³⋊(C₄⋊C₄)	The semidirect product of C₃³ and C₄⋊C₄ acting via C₄⋊C₄/C₂=C₂×C₄	48	8-	C3^3:(C4:C4)	432,569
S₃×C₃²⋊₂C₈	Direct product of S₃ and C₃²⋊₂C₈	48	8-	S3xC3^2:2C8	432,570
C₃³⋊M₄(2)	1^st semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₂=C₂×C₄	48	8-	C3^3:M4(2)	432,572
C₃×C₃⋊S₃.Q₈	Direct product of C₃ and C₃⋊S₃.Q₈	48	4	C3xC3:S3.Q8	432,575
C₃×C₃²⋊Q₁₆	Direct product of C₃ and C₃²⋊Q₁₆	48	4	C3xC3^2:Q16	432,578
C₃³⋊C₄⋊C₄	2^nd semidirect product of C₃³⋊C₄ and C₄ acting via C₄/C₂=C₂	48	4	C3^3:C4:C4	432,581
C₃³⋊Q₁₆	2^nd semidirect product of C₃³ and Q₁₆ acting via Q₁₆/C₂=D₄	48	4	C3^3:Q16	432,585
(C₃×C₆).₉D₁₂	2^nd non-split extension by C₃×C₆ of D₁₂ acting via D₁₂/C₃=D₄	48	8-	(C3xC6).9D12	432,587
C₃³⋊₃Q₁₆	3^rd semidirect product of C₃³ and Q₁₆ acting via Q₁₆/C₂=D₄	48	8-	C3^3:3Q16	432,590
C₃×C₂.PSU₃(𝔽₂)	Direct product of C₃ and C₂.PSU₃(𝔽₂)	48	8	C3xC2.PSU(3,2)	432,591
C₆.PSU₃(𝔽₂)	1^st non-split extension by C₆ of PSU₃(𝔽₂) acting via PSU₃(𝔽₂)/C₃²⋊C₄=C₂	48	8	C6.PSU(3,2)	432,592
C₆.₂PSU₃(𝔽₂)	2^nd non-split extension by C₆ of PSU₃(𝔽₂) acting via PSU₃(𝔽₂)/C₃²⋊C₄=C₂	48	8	C6.2PSU(3,2)	432,593
S₃²×Dic₃	Direct product of S₃, S₃ and Dic₃	48	8-	S3^2xDic3	432,594
Dic₃⋊₆S₃²	2^nd semidirect product of Dic₃ and S₃² acting through Inn(Dic₃)	48	8-	Dic3:6S3^2	432,596
S₃×D₆⋊S₃	Direct product of S₃ and D₆⋊S₃	48	8-	S3xD6:S3	432,597
D₆⋊S₃²	3^rd semidirect product of D₆ and S₃² acting via S₃²/C₃×S₃=C₂	48	8-	D6:S3^2	432,600
S₃×C₃²⋊₂Q₈	Direct product of S₃ and C₃²⋊₂Q₈	48	8-	S3xC3^2:2Q8	432,603
C₃³⋊₅(C₂×Q₈)	2^nd semidirect product of C₃³ and C₂×Q₈ acting via C₂×Q₈/C₂=C₂³	48	8-	C3^3:5(C2xQ8)	432,604
D₆.S₃²	2^nd non-split extension by D₆ of S₃² acting via S₃²/C₃×S₃=C₂	48	8-	D6.S3^2	432,607
D₆.₄S₃²	1^st non-split extension by D₆ of S₃² acting via S₃²/C₃⋊S₃=C₂	48	8-	D6.4S3^2	432,608
D₆⋊S₃⋊S₃	5^th semidirect product of D₆⋊S₃ and S₃ acting via S₃/C₃=C₂	48	8-	D6:S3:S3	432,610
D₆.₆S₃²	3^rd non-split extension by D₆ of S₃² acting via S₃²/C₃⋊S₃=C₂	48	8-	D6.6S3^2	432,611
C₃×C₆.₅S₄	Direct product of C₃ and C₆.₅S₄	48	4	C3xC6.5S4	432,616
C₃×C₆.₆S₄	Direct product of C₃ and C₆.₆S₄	48	4	C3xC6.6S4	432,617
C₃×Dic₃.A₄	Direct product of C₃ and Dic₃.A₄	48	4	C3xDic3.A4	432,622
C₃×S₃×SL₂(𝔽₃)	Direct product of C₃, S₃ and SL₂(𝔽₃)	48	4	C3xS3xSL(2,3)	432,623
C₃×C₃⋊S₃⋊₃C₈	Direct product of C₃ and C₃⋊S₃⋊₃C₈	48	4	C3xC3:S3:3C8	432,628
C₃×C₃²⋊M₄(2)	Direct product of C₃ and C₃²⋊M₄(2)	48	4	C3xC3^2:M4(2)	432,629
C₁₂×C₃²⋊C₄	Direct product of C₁₂ and C₃²⋊C₄	48	4	C12xC3^2:C4	432,630
C₃×C₄⋊(C₃²⋊C₄)	Direct product of C₃ and C₄⋊(C₃²⋊C₄)	48	4	C3xC4:(C3^2:C4)	432,631
C₆×C₃²⋊₂C₈	Direct product of C₆ and C₃²⋊₂C₈	48		C6xC3^2:2C8	432,632
C₃³⋊₇(C₂×C₈)	2^nd semidirect product of C₃³ and C₂×C₈ acting via C₂×C₈/C₄=C₄	48	4	C3^3:7(C2xC8)	432,635
C₃³⋊₄M₄(2)	2^nd semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₄=C₄	48	4	C3^3:4M4(2)	432,636
C₄×C₃³⋊C₄	Direct product of C₄ and C₃³⋊C₄	48	4	C4xC3^3:C4	432,637
C₃³⋊₉(C₄⋊C₄)	2^nd semidirect product of C₃³ and C₄⋊C₄ acting via C₄⋊C₄/C₄=C₄	48	4	C3^3:9(C4:C4)	432,638
C₂×C₃³⋊₄C₈	Direct product of C₂ and C₃³⋊₄C₈	48		C2xC3^3:4C8	432,639
C₃×S₃×Dic₆	Direct product of C₃, S₃ and Dic₆	48	4	C3xS3xDic6	432,642
C₃×D₁₂⋊₅S₃	Direct product of C₃ and D₁₂⋊₅S₃	48	4	C3xD12:5S3	432,643
C₃×D₁₂⋊S₃	Direct product of C₃ and D₁₂⋊S₃	48	4	C3xD12:S3	432,644
C₃×Dic₃.D₆	Direct product of C₃ and Dic₃.D₆	48	4	C3xDic3.D6	432,645
C₃×D₆.D₆	Direct product of C₃ and D₆.D₆	48	4	C3xD6.D6	432,646
C₃×D₆.₆D₆	Direct product of C₃ and D₆.₆D₆	48	4	C3xD6.6D6	432,647
S₃²×C₁₂	Direct product of C₁₂, S₃ and S₃	48	4	S3^2xC12	432,648
C₃×S₃×D₁₂	Direct product of C₃, S₃ and D₁₂	48	4	C3xS3xD12	432,649
C₃×D₆⋊D₆	Direct product of C₃ and D₆⋊D₆	48	4	C3xD6:D6	432,650
S₃×C₆×Dic₃	Direct product of C₆, S₃ and Dic₃	48		S3xC6xDic3	432,651
C₆×C₆.D₆	Direct product of C₆ and C₆.D₆	48		C6xC6.D6	432,654
C₆×D₆⋊S₃	Direct product of C₆ and D₆⋊S₃	48		C6xD6:S3	432,655
C₆×C₃⋊D₁₂	Direct product of C₆ and C₃⋊D₁₂	48		C6xC3:D12	432,656
C₆×C₃²⋊₂Q₈	Direct product of C₆ and C₃²⋊₂Q₈	48		C6xC3^2:2Q8	432,657
C₃⋊S₃⋊₄Dic₆	The semidirect product of C₃⋊S₃ and Dic₆ acting via Dic₆/C₁₂=C₂	48	4	C3:S3:4Dic6	432,687
C₁₂⋊S₃⋊₁₂S₃	6^th semidirect product of C₁₂⋊S₃ and S₃ acting via S₃/C₃=C₂	48	4	C12:S3:12S3	432,688
C₁₂.₉₅S₃²	15^th non-split extension by C₁₂ of S₃² acting via S₃²/C₃⋊S₃=C₂	48	4	C12.95S3^2	432,689
C₄×C₃²⋊₄D₆	Direct product of C₄ and C₃²⋊₄D₆	48	4	C4xC3^2:4D6	432,690
C₁₂⋊₃S₃²	3^rd semidirect product of C₁₂ and S₃² acting via S₃²/C₃²=C₂²	48	4	C12:3S3^2	432,691
C₂×C₃³⋊₉(C₂×C₄)	Direct product of C₂ and C₃³⋊₉(C₂×C₄)	48		C2xC3^3:9(C2xC4)	432,692
C₂×C₃³⋊₉D₄	Direct product of C₂ and C₃³⋊₉D₄	48		C2xC3^3:9D4	432,694
C₂×C₃³⋊₅Q₈	Direct product of C₂ and C₃³⋊₅Q₈	48		C2xC3^3:5Q8	432,695
C₆×F₉	Direct product of C₆ and F₉	48	8	C6xF9	432,751
C₂×C₃⋊F₉	Direct product of C₂ and C₃⋊F₉	48	8	C2xC3:F9	432,752
C₆×PSU₃(𝔽₂)	Direct product of C₆ and PSU₃(𝔽₂)	48	8	C6xPSU(3,2)	432,757
C₂×C₃³⋊Q₈	Direct product of C₂ and C₃³⋊Q₈	48	8	C2xC3^3:Q8	432,758
C₂×C₆×C₃²⋊C₄	Direct product of C₂×C₆ and C₃²⋊C₄	48		C2xC6xC3^2:C4	432,765
C₂²×C₃³⋊C₄	Direct product of C₂² and C₃³⋊C₄	48		C2^2xC3^3:C4	432,766
S₃²×C₂×C₆	Direct product of C₂×C₆, S₃ and S₃	48		S3^2xC2xC6	432,767
C₂²×C₃²⋊₄D₆	Direct product of C₂² and C₃²⋊₄D₆	48		C2^2xC3^2:4D6	432,769

Groups of order 480

		d	ρ	Label	ID
C₈.A₅	The central extension by C₈ of A₅	48	2	C8.A5	480,221
C₄.₆S₅	3^rd central extension by C₄ of S₅	48	4	C4.6S5	480,946
C₄.S₅	2^nd non-split extension by C₄ of S₅ acting via S₅/A₅=C₂	48	4	C4.S5	480,947
C₂².S₅	The non-split extension by C₂² of S₅ acting via S₅/A₅=C₂	48	4-	C2^2.S5	480,953
C₂×C₄.A₅	Direct product of C₂ and C₄.A₅	48		C2xC4.A5	480,955
D₄.A₅	The non-split extension by D₄ of A₅ acting through Inn(D₄)	48	4-	D4.A5	480,957
Q₈.A₅	The non-split extension by Q₈ of A₅ acting through Inn(Q₈)	48	4+	Q8.A5	480,959

On 49 points

Groups of order 49

		d	ρ	Label	ID
C₄₉	Cyclic group	49	1	C49	49,1
C₇²	Elementary abelian group of type [7,7]	49		C7^2	49,2

Groups of order 98

		d	ρ	Label	ID
D₄₉	Dihedral group	49	2+	D49	98,1
C₇⋊D₇	The semidirect product of C₇ and D₇ acting via D₇/C₇=C₂	49		C7:D7	98,4

Groups of order 147

		d	ρ	Label	ID
C₄₉⋊C₃	The semidirect product of C₄₉ and C₃ acting faithfully	49	3	C49:C3	147,1
C₇²⋊C₃	2^nd semidirect product of C₇² and C₃ acting faithfully	49		C7^2:C3	147,4

Groups of order 294

		d	ρ	Label	ID
C₄₉⋊C₆	The semidirect product of C₄₉ and C₆ acting faithfully	49	6+	C49:C6	294,1
C₇⋊F₇	1^st semidirect product of C₇ and F₇ acting via F₇/C₇=C₆	49		C7:F7	294,13

Groups of order 343

		d	ρ	Label	ID
He₇	Heisenberg group; = C₇² ⋊C₇ = 7₊¹⁺²	49	7	He7	343,3
7_-¹⁺²	Extraspecial group	49	7	ES-(7,1)	343,4

On 50 points

Groups of order 50

		d	ρ	Label	ID
C₅₀	Cyclic group	50	1	C50	50,2
C₅×C₁₀	Abelian group of type [5,10]	50		C5xC10	50,5

Groups of order 100

		d	ρ	Label	ID
D₅₀	Dihedral group; = C₂×D₂₅	50	2+	D50	100,4
C₂×C₅⋊D₅	Direct product of C₂ and C₅⋊D₅	50		C2xC5:D5	100,15

Groups of order 200

		d	ρ	Label	ID
C₂×C₂₅⋊C₄	Direct product of C₂ and C₂₅⋊C₄	50	4+	C2xC25:C4	200,12
C₂×C₅⋊F₅	Direct product of C₂ and C₅⋊F₅	50		C2xC5:F5	200,47

Groups of order 250

		d	ρ	Label	ID
C₅×D₂₅	Direct product of C₅ and D₂₅	50	2	C5xD25	250,3
D₅×C₂₅	Direct product of C₂₅ and D₅	50	2	D5xC25	250,4
C₂×He₅	Direct product of C₂ and He₅	50	5	C2xHe5	250,10
C₂×5_-¹⁺²	Direct product of C₂ and 5_-¹⁺²	50	5	C2xES-(5,1)	250,11
D₅×C₅²	Direct product of C₅² and D₅	50		D5xC5^2	250,12
C₅×C₅⋊D₅	Direct product of C₅ and C₅⋊D₅	50		C5xC5:D5	250,13

Groups of order 400

		d	ρ	Label	ID
C₂⁴⋊C₂₅	The semidirect product of C₂⁴ and C₂₅ acting via C₂₅/C₅=C₅	50	5	C2^4:C25	400,52
C₅×C₂⁴⋊C₅	Direct product of C₅ and C₂⁴⋊C₅	50	5	C5xC2^4:C5	400,213

Groups of order 500

		d	ρ	Label	ID
C₂₅⋊₂F₅	2^nd semidirect product of C₂₅ and F₅ acting via F₅/C₅=C₄	50	4+	C25:2F5	500,24
D₅×D₂₅	Direct product of D₅ and D₂₅	50	4+	D5xD25	500,26
C₂×C₅²⋊C₁₀	Direct product of C₂ and C₅²⋊C₁₀	50	10+	C2xC5^2:C10	500,30
C₂×C₂₅⋊C₁₀	Direct product of C₂ and C₂₅⋊C₁₀	50	10+	C2xC25:C10	500,31
C₂×He₅⋊C₂	Direct product of C₂ and He₅⋊C₂	50	5	C2xHe5:C2	500,33
C₅³⋊₉C₄	9^th semidirect product of C₅³ and C₄ acting faithfully	50		C5^3:9C4	500,49
D₅×C₅⋊D₅	Direct product of D₅ and C₅⋊D₅	50		D5xC5:D5	500,51

On 51 points

Groups of order 51

		d	ρ	Label	ID
C₅₁	Cyclic group	51	1	C51	51,1

Groups of order 102

		d	ρ	Label	ID
S₃×C₁₇	Direct product of C₁₇ and S₃	51	2	S3xC17	102,1
C₃×D₁₇	Direct product of C₃ and D₁₇	51	2	C3xD17	102,2
D₅₁	Dihedral group	51	2+	D51	102,3

Groups of order 204

		d	ρ	Label	ID
C₃×C₁₇⋊C₄	Direct product of C₃ and C₁₇⋊C₄	51	4	C3xC17:C4	204,5
C₅₁⋊C₄	1^st semidirect product of C₅₁ and C₄ acting faithfully	51	4	C51:C4	204,6
S₃×D₁₇	Direct product of S₃ and D₁₇	51	4+	S3xD17	204,7

Groups of order 408

		d	ρ	Label	ID
C₃×C₁₇⋊C₈	Direct product of C₃ and C₁₇⋊C₈	51	8	C3xC17:C8	408,33
C₅₁⋊C₈	1^st semidirect product of C₅₁ and C₈ acting faithfully	51	8	C51:C8	408,34
S₃×C₁₇⋊C₄	Direct product of S₃ and C₁₇⋊C₄	51	8+	S3xC17:C4	408,35

On 52 points

Groups of order 52

		d	ρ	Label	ID
Dic₁₃	Dicyclic group; = C₁₃ ⋊₂ C₄	52	2-	Dic13	52,1
C₅₂	Cyclic group	52	1	C52	52,2
C₂×C₂₆	Abelian group of type [2,26]	52		C2xC26	52,5

Groups of order 104

		d	ρ	Label	ID
C₄×D₁₃	Direct product of C₄ and D₁₃	52	2	C4xD13	104,5
D₅₂	Dihedral group	52	2+	D52	104,6
C₁₃⋊D₄	The semidirect product of C₁₃ and D₄ acting via D₄/C₂²=C₂	52	2	C13:D4	104,8
D₄×C₁₃	Direct product of C₁₃ and D₄	52	2	D4xC13	104,10
C₂²×D₁₃	Direct product of C₂² and D₁₃	52		C2^2xD13	104,13

Groups of order 156

		d	ρ	Label	ID
C₂₆.C₆	The non-split extension by C₂₆ of C₆ acting faithfully	52	6-	C26.C6	156,1
C₄×C₁₃⋊C₃	Direct product of C₄ and C₁₃⋊C₃	52	3	C4xC13:C3	156,2
C₂²×C₁₃⋊C₃	Direct product of C₂² and C₁₃⋊C₃	52		C2^2xC13:C3	156,12
A₄×C₁₃	Direct product of C₁₃ and A₄	52	3	A4xC13	156,13
C₁₃⋊A₄	The semidirect product of C₁₃ and A₄ acting via A₄/C₂²=C₃	52	3	C13:A4	156,14

Groups of order 208

		d	ρ	Label	ID
C₄×C₁₃⋊C₄	Direct product of C₄ and C₁₃⋊C₄	52	4	C4xC13:C4	208,30
C₅₂⋊C₄	1^st semidirect product of C₅₂ and C₄ acting faithfully	52	4	C52:C4	208,31
D₁₃.D₄	The non-split extension by D₁₃ of D₄ acting via D₄/C₂²=C₂	52	4+	D13.D4	208,34
D₄×D₁₃	Direct product of D₄ and D₁₃	52	4+	D4xD13	208,39
C₂²×C₁₃⋊C₄	Direct product of C₂² and C₁₃⋊C₄	52		C2^2xC13:C4	208,49

Groups of order 312

		d	ρ	Label	ID
C₄×C₁₃⋊C₆	Direct product of C₄ and C₁₃⋊C₆	52	6	C4xC13:C6	312,9
D₅₂⋊C₃	The semidirect product of D₅₂ and C₃ acting faithfully	52	6+	D52:C3	312,10
D₂₆⋊C₆	2^nd semidirect product of D₂₆ and C₆ acting faithfully	52	6	D26:C6	312,12
D₄×C₁₃⋊C₃	Direct product of D₄ and C₁₃⋊C₃	52	6	D4xC13:C3	312,23
C₁₃×S₄	Direct product of C₁₃ and S₄	52	3	C13xS4	312,47
C₁₃⋊S₄	The semidirect product of C₁₃ and S₄ acting via S₄/A₄=C₂	52	6+	C13:S4	312,48
C₂²×C₁₃⋊C₆	Direct product of C₂² and C₁₃⋊C₆	52		C2^2xC13:C6	312,49
A₄×D₁₃	Direct product of A₄ and D₁₃	52	6+	A4xD13	312,50
D₁₃⋊A₄	The semidirect product of D₁₃ and A₄ acting via A₄/C₂²=C₃	52	6+	D13:A4	312,51

Groups of order 416

		d	ρ	Label	ID
D₄×C₁₃⋊C₄	Direct product of D₄ and C₁₃⋊C₄	52	8+	D4xC13:C4	416,206

Groups of order 468

		d	ρ	Label	ID
A₄×C₁₃⋊C₃	Direct product of A₄ and C₁₃⋊C₃	52	9	A4xC13:C3	468,32

On 53 points

Groups of order 53

		d	ρ	Label	ID
C₅₃	Cyclic group	53	1	C53	53,1

Groups of order 106

		d	ρ	Label	ID
D₅₃	Dihedral group	53	2+	D53	106,1

Groups of order 212

		d	ρ	Label	ID
C₅₃⋊C₄	The semidirect product of C₅₃ and C₄ acting faithfully	53	4+	C53:C4	212,3

On 54 points

Groups of order 54

		d	ρ	Label	ID
C₅₄	Cyclic group	54	1	C54	54,2
C₃×C₁₈	Abelian group of type [3,18]	54		C3xC18	54,9
C₃²×C₆	Abelian group of type [3,3,6]	54		C3^2xC6	54,15

Groups of order 108

		d	ρ	Label	ID
C₉.A₄	The central extension by C₉ of A₄	54	3	C9.A4	108,3
D₅₄	Dihedral group; = C₂×D₂₇	54	2+	D54	108,4
C₃×C₃.A₄	Direct product of C₃ and C₃.A₄	54		C3xC3.A4	108,20
C₂×C₉⋊S₃	Direct product of C₂ and C₉⋊S₃	54		C2xC9:S3	108,27
C₂×C₃³⋊C₂	Direct product of C₂ and C₃³⋊C₂	54		C2xC3^3:C2	108,44

Groups of order 162

		d	ρ	Label	ID
C₃×D₂₇	Direct product of C₃ and D₂₇	54	2	C3xD27	162,7
S₃×C₂₇	Direct product of C₂₇ and S₃	54	2	S3xC27	162,8
C₂×C₃²⋊C₉	Direct product of C₂ and C₃²⋊C₉	54		C2xC3^2:C9	162,24
C₂×C₂₇⋊C₃	Direct product of C₂ and C₂₇⋊C₃	54	3	C2xC27:C3	162,27
C₂×He₃.C₃	Direct product of C₂ and He₃.C₃	54	3	C2xHe3.C3	162,29
C₂×He₃⋊C₃	Direct product of C₂ and He₃⋊C₃	54	3	C2xHe3:C3	162,30
C₂×C₃.He₃	Direct product of C₂ and C₃.He₃	54	3	C2xC3.He3	162,31
C₃²×D₉	Direct product of C₃² and D₉	54		C3^2xD9	162,32
S₃×C₃×C₉	Direct product of C₃×C₉ and S₃	54		S3xC3xC9	162,33
C₃×C₉⋊S₃	Direct product of C₃ and C₉⋊S₃	54		C3xC9:S3	162,38
C₉×C₃⋊S₃	Direct product of C₉ and C₃⋊S₃	54		C9xC3:S3	162,39
C₆×He₃	Direct product of C₆ and He₃	54		C6xHe3	162,48
C₆×3_-¹⁺²	Direct product of C₆ and 3_-¹⁺²	54		C6xES-(3,1)	162,49
C₂×C₉○He₃	Direct product of C₂ and C₉○He₃	54	3	C2xC9oHe3	162,50
S₃×C₃³	Direct product of C₃³ and S₃	54		S3xC3^3	162,51
C₃×C₃³⋊C₂	Direct product of C₃ and C₃³⋊C₂	54		C3xC3^3:C2	162,53

Groups of order 216

		d	ρ	Label	ID
C₉.S₄	The non-split extension by C₉ of S₄ acting via S₄/A₄=C₂	54	6+	C9.S4	216,21
C₂×C₉.A₄	Direct product of C₂ and C₉.A₄	54	3	C2xC9.A4	216,22
C₃².₃S₄	2^nd non-split extension by C₃² of S₄ acting via S₄/A₄=C₂	54		C3^2.3S4	216,94
A₄×C₁₈	Direct product of C₁₈ and A₄	54	3	A4xC18	216,103
C₂×C₉⋊A₄	Direct product of C₂ and C₉⋊A₄	54	3	C2xC9:A4	216,104
C₆×C₃.A₄	Direct product of C₆ and C₃.A₄	54		C6xC3.A4	216,105
A₄×C₃×C₆	Direct product of C₃×C₆ and A₄	54		A4xC3xC6	216,173

Groups of order 324

		d	ρ	Label	ID
S₃×D₂₇	Direct product of S₃ and D₂₇	54	4+	S3xD27	324,38
C₆².C₉	2^nd non-split extension by C₆² of C₉ acting via C₉/C₃=C₃	54	3	C6^2.C9	324,45
C₆².₁₃C₃²	4^th non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	54	3	C6^2.13C3^2	324,49
C₆².₁₄C₃²	5^th non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	54	3	C6^2.14C3^2	324,50
C₆².₁₅C₃²	6^th non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	54	3	C6^2.15C3^2	324,51
He₃.A₄	The non-split extension by He₃ of A₄ acting via A₄/C₂²=C₃	54	9	He3.A4	324,53
He₃⋊A₄	1^st semidirect product of He₃ and A₄ acting via A₄/C₂²=C₃	54	9	He3:A4	324,54
C₆².C₃²	4^th non-split extension by C₆² of C₃² acting faithfully	54	9	C6^2.C3^2	324,56
3_-¹⁺²⋊A₄	1^st semidirect product of 3_-¹⁺² and A₄ acting via A₄/C₂²=C₃	54	9	ES-(3,1):A4	324,57
C₆²⋊C₉	1^st semidirect product of C₆² and C₉ acting via C₉/C₃=C₃	54		C6^2:C9	324,59
C₂×C₃²⋊D₉	Direct product of C₂ and C₃²⋊D₉	54		C2xC3^2:D9	324,63
C₂×C₂₇⋊C₆	Direct product of C₂ and C₂₇⋊C₆	54	6+	C2xC27:C6	324,67
C₂×He₃.C₆	Direct product of C₂ and He₃.C₆	54	3	C2xHe3.C6	324,70
C₂×He₃.S₃	Direct product of C₂ and He₃.S₃	54	6+	C2xHe3.S3	324,71
C₂×He₃.₂C₆	Direct product of C₂ and He₃.₂C₆	54	3	C2xHe3.2C6	324,72
C₂×He₃.₂S₃	Direct product of C₂ and He₃.₂S₃	54	6+	C2xHe3.2S3	324,73
C₂×He₃.₃S₃	Direct product of C₂ and He₃.₃S₃	54	6+	C2xHe3.3S3	324,78
C₂×He₃⋊S₃	Direct product of C₂ and He₃⋊S₃	54	6+	C2xHe3:S3	324,79
C₂×3_-¹⁺².S₃	Direct product of C₂ and 3_-¹⁺².S₃	54	6+	C2xES-(3,1).S3	324,80
C₃×He₃⋊C₄	Direct product of C₃ and He₃⋊C₄	54		C3xHe3:C4	324,110
He₃.₃C₁₂	The non-split extension by He₃ of C₁₂ acting via C₁₂/C₃=C₄	54	3	He3.3C12	324,111
D₉×C₃⋊S₃	Direct product of D₉ and C₃⋊S₃	54		D9xC3:S3	324,119
S₃×C₉⋊S₃	Direct product of S₃ and C₉⋊S₃	54		S3xC9:S3	324,120
C₆².₂₅C₃²	16^th non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	54	3	C6^2.25C3^2	324,128
He₃.₂A₄	The non-split extension by He₃ of A₄ acting through Inn(He₃)	54	9	He3.2A4	324,129
C₆².₉C₃²	9^th non-split extension by C₆² of C₃² acting faithfully	54	9	C6^2.9C3^2	324,132
C₃×C₃².A₄	Direct product of C₃ and C₃².A₄	54		C3xC3^2.A4	324,134
C₃×C₃²⋊A₄	Direct product of C₃ and C₃²⋊A₄	54		C3xC3^2:A4	324,135
C₂×He₃⋊₄S₃	Direct product of C₂ and He₃⋊₄S₃	54		C2xHe3:4S3	324,144
C₆×He₃⋊C₂	Direct product of C₆ and He₃⋊C₂	54		C6xHe3:C2	324,145
C₂×C₃³.S₃	Direct product of C₂ and C₃³.S₃	54		C2xC3^3.S3	324,146
C₂×He₃.₄S₃	Direct product of C₂ and He₃.₄S₃	54	6+	C2xHe3.4S3	324,147
C₂×He₃.₄C₆	Direct product of C₂ and He₃.₄C₆	54	3	C2xHe3.4C6	324,148
S₃×C₃³⋊C₂	Direct product of S₃ and C₃³⋊C₂	54		S3xC3^3:C2	324,168

Groups of order 432

		d	ρ	Label	ID
C₂×C₉.S₄	Direct product of C₂ and C₉.S₄	54	6+	C2xC9.S4	432,224
A₄×C₃.A₄	Direct product of A₄ and C₃.A₄	54	9	A4xC3.A4	432,524
C₂⁴⋊3_-¹⁺²	1^st semidirect product of C₂⁴ and 3_-¹⁺² acting via 3_-¹⁺²/C₃=C₃²	54	9	C2^4:ES-(3,1)	432,527
C₂×He₃⋊C₈	Direct product of C₂ and He₃⋊C₈	54	6+	C2xHe3:C8	432,529
C₂×SU₃(𝔽₂)	Direct product of C₂ and SU₃(𝔽₂)	54	3	C2xSU(3,2)	432,531
C₁₈×S₄	Direct product of C₁₈ and S₄	54	3	C18xS4	432,532
C₂×C₉⋊S₄	Direct product of C₂ and C₉⋊S₄	54	6+	C2xC9:S4	432,536
C₂×C₃².₃S₄	Direct product of C₂ and C₃².₃S₄	54		C2xC3^2.3S4	432,537
C₂×D₉⋊A₄	Direct product of C₂ and D₉⋊A₄	54	6+	C2xD9:A4	432,539
C₂×A₄×D₉	Direct product of C₂, A₄ and D₉	54	6+	C2xA4xD9	432,540
C₃×C₆×S₄	Direct product of C₃×C₆ and S₄	54		C3xC6xS4	432,760
C₂×C₃²⋊₄S₄	Direct product of C₂ and C₃²⋊₄S₄	54		C2xC3^2:4S4	432,762
C₂×A₄×C₃⋊S₃	Direct product of C₂, A₄ and C₃⋊S₃	54		C2xA4xC3:S3	432,764

Groups of order 486

		d	ρ	Label	ID
C₉⋊S₃⋊C₉	1^st semidirect product of C₉⋊S₃ and C₉ acting via C₉/C₃=C₃	54		C9:S3:C9	486,3
C₃.C₃≀S₃	1^st non-split extension by C₃ of C₃≀S₃ acting via C₃≀S₃/C₃≀C₃=C₂	54	6	C3.C3wrS3	486,4
C₃.₃C₃≀S₃	3^rd non-split extension by C₃ of C₃≀S₃ acting via C₃≀S₃/C₃≀C₃=C₂	54	6	C3.3C3wrS3	486,8
(C₃×He₃).C₆	2^nd non-split extension by C₃×He₃ of C₆ acting faithfully	54	6	(C3xHe3).C6	486,9
C₃²⋊C₉.C₆	2^nd non-split extension by C₃²⋊C₉ of C₆ acting faithfully	54	6	C3^2:C9.C6	486,10
C₃³.(C₃×S₃)	8^th non-split extension by C₃³ of C₃×S₃ acting faithfully	54	6	C3^3.(C3xS3)	486,11
C₃²⋊₂D₉.C₃	3^rd non-split extension by C₃²⋊₂D₉ of C₃ acting faithfully	54	6	C3^2:2D9.C3	486,12
C₉×D₂₇	Direct product of C₉ and D₂₇	54	2	C9xD27	486,13
D₉×C₂₇	Direct product of C₂₇ and D₉	54	2	D9xC27	486,14
C₂₇⋊₃C₁₈	The semidirect product of C₂₇ and C₁₈ acting via C₁₈/C₃=C₆	54	6	C27:3C18	486,15
C₃²⋊C₅₄	The semidirect product of C₃² and C₅₄ acting via C₅₄/C₉=C₆	54	6	C3^2:C54	486,16
(C₃×C₉)⋊C₁₈	2^nd semidirect product of C₃×C₉ and C₁₈ acting via C₁₈/C₃=C₆	54	6	(C3xC9):C18	486,20
(C₃×C₉)⋊D₉	2^nd semidirect product of C₃×C₉ and D₉ acting via D₉/C₃=S₃	54	6	(C3xC9):D9	486,21
C₉⋊S₃⋊₃C₉	3^rd semidirect product of C₉⋊S₃ and C₉ acting via C₉/C₃=C₃	54	6	C9:S3:3C9	486,22
(C₃×C₉)⋊₃D₉	3^rd semidirect product of C₃×C₉ and D₉ acting via D₉/C₃=S₃	54	6	(C3xC9):3D9	486,23
C₉⋊C₅₄	The semidirect product of C₉ and C₅₄ acting via C₅₄/C₉=C₆	54	6	C9:C54	486,30
C₃²⋊₂D₂₇	2^nd semidirect product of C₃² and D₂₇ acting via D₂₇/C₉=S₃	54	6	C3^2:2D27	486,51
C₂×C₃³⋊C₉	Direct product of C₂ and C₃³⋊C₉	54		C2xC3^3:C9	486,73
C₂×C₉.₄He₃	Direct product of C₂ and C₉.₄He₃	54	3	C2xC9.4He3	486,76
C₂×C₂₇⋊C₉	Direct product of C₂ and C₂₇⋊C₉	54	9	C2xC27:C9	486,82
C₂×C₉²⋊C₃	Direct product of C₂ and C₉²⋊C₃	54	3	C2xC9^2:C3	486,85
C₂×C₉²⋊₂C₃	Direct product of C₂ and C₉²⋊₂C₃	54	3	C2xC9^2:2C3	486,86
C₂×C₉².C₃	Direct product of C₂ and C₉².C₃	54	3	C2xC9^2.C3	486,87
C₂×C₃².He₃	Direct product of C₂ and C₃².He₃	54	9	C2xC3^2.He3	486,88
C₂×C₃².₅He₃	Direct product of C₂ and C₃².₅He₃	54	9	C2xC3^2.5He3	486,89
C₂×C₃².₆He₃	Direct product of C₂ and C₃².₆He₃	54	9	C2xC3^2.6He3	486,90
D₉×C₃×C₉	Direct product of C₃×C₉ and D₉	54		D9xC3xC9	486,91
C₃×C₃²⋊C₁₈	Direct product of C₃ and C₃²⋊C₁₈	54		C3xC3^2:C18	486,93
C₃×C₃²⋊D₉	Direct product of C₃ and C₃²⋊D₉	54		C3xC3^2:D9	486,94
S₃×C₃²⋊C₉	Direct product of S₃ and C₃²⋊C₉	54		S3xC3^2:C9	486,95
C₃×C₉⋊C₁₈	Direct product of C₃ and C₉⋊C₁₈	54		C3xC9:C18	486,96
C₉×C₃²⋊C₆	Direct product of C₉ and C₃²⋊C₆	54	6	C9xC3^2:C6	486,98
D₉×He₃	Direct product of D₉ and He₃	54	6	D9xHe3	486,99
C₉×C₉⋊C₆	Direct product of C₉ and C₉⋊C₆	54	6	C9xC9:C6	486,100
D₉×3_-¹⁺²	Direct product of D₉ and 3_-¹⁺²	54	6	D9xES-(3,1)	486,101
D₉⋊He₃	The semidirect product of D₉ and He₃ acting via He₃/C₃²=C₃	54	6	D9:He3	486,106
C₉⋊He₃⋊C₂	3^rd semidirect product of C₉⋊He₃ and C₂ acting faithfully	54	6	C9:He3:C2	486,107
D₉⋊3_-¹⁺²	The semidirect product of D₉ and 3_-¹⁺² acting via 3_-¹⁺²/C₃²=C₃	54	6	D9:ES-(3,1)	486,108
C₉²⋊₇C₆	7^th semidirect product of C₉² and C₆ acting faithfully	54	6	C9^2:7C6	486,109
C₃×C₂₇⋊C₆	Direct product of C₃ and C₂₇⋊C₆	54	6	C3xC27:C6	486,113
S₃×C₂₇⋊C₃	Direct product of S₃ and C₂₇⋊C₃	54	6	S3xC27:C3	486,114
C₃×He₃.S₃	Direct product of C₃ and He₃.S₃	54	6	C3xHe3.S3	486,119
S₃×He₃.C₃	Direct product of S₃ and He₃.C₃	54	6	S3xHe3.C3	486,120
C₃×He₃.₂S₃	Direct product of C₃ and He₃.₂S₃	54	6	C3xHe3.2S3	486,122
S₃×He₃⋊C₃	Direct product of S₃ and He₃⋊C₃	54	6	S3xHe3:C3	486,123
S₃×C₃.He₃	Direct product of S₃ and C₃.He₃	54	6	S3xC3.He3	486,124
C₉×C₉⋊S₃	Direct product of C₉ and C₉⋊S₃	54		C9xC9:S3	486,133
C₃×C₃²⋊₂D₉	Direct product of C₃ and C₃²⋊₂D₉	54		C3xC3^2:2D9	486,135
C₃³⋊C₁₈	4^th semidirect product of C₃³ and C₁₈ acting via C₁₈/C₃=C₆	54		C3^3:C18	486,136
C₉⋊(S₃×C₉)	The semidirect product of C₉ and S₃×C₉ acting via S₃×C₉/C₃²=C₆	54		C9:(S3xC9)	486,138
C₉²⋊₃S₃	3^rd semidirect product of C₉² and S₃ acting faithfully	54	6	C9^2:3S3	486,139
C₉²⋊₄S₃	4^th semidirect product of C₉² and S₃ acting faithfully	54	6	C9^2:4S3	486,140
(C₃²×C₉)⋊S₃	14^th semidirect product of C₃²×C₉ and S₃ acting faithfully	54	6	(C3^2xC9):S3	486,149
(C₃²×C₉)⋊₈S₃	8^th semidirect product of C₃²×C₉ and S₃ acting faithfully	54	6	(C3^2xC9):8S3	486,150
C₉⋊C₉⋊₂S₃	2^nd semidirect product of C₉⋊C₉ and S₃ acting faithfully	54	6	C9:C9:2S3	486,152
C₉²⋊₅S₃	5^th semidirect product of C₉² and S₃ acting faithfully	54	6	C9^2:5S3	486,156
C₃×He₃.₃S₃	Direct product of C₃ and He₃.₃S₃	54	6	C3xHe3.3S3	486,168
He₃.C₃⋊S₃	5^th semidirect product of He₃.C₃ and S₃ acting via S₃/C₃=C₂	54	6	He3.C3:S3	486,169
C₃×He₃⋊S₃	Direct product of C₃ and He₃⋊S₃	54	6	C3xHe3:S3	486,171
He₃⋊C₃⋊₂S₃	1^st semidirect product of He₃⋊C₃ and S₃ acting via S₃/C₃=C₂	54	6	He3:C3:2S3	486,172
C₃×3_-¹⁺².S₃	Direct product of C₃ and 3_-¹⁺².S₃	54	6	C3xES-(3,1).S3	486,174
C₃³⋊₆D₉	6^th semidirect product of C₃³ and D₉ acting via D₉/C₃=S₃	54		C3^3:6D9	486,181
He₃⋊₄D₉	2^nd semidirect product of He₃ and D₉ acting via D₉/C₉=C₂	54	6	He3:4D9	486,182
C₂×C₃²⋊He₃	Direct product of C₂ and C₃²⋊He₃	54		C2xC3^2:He3	486,196
C₂×C₃⁴.C₃	Direct product of C₂ and C₃⁴.C₃	54		C2xC3^4.C3	486,197
C₆×C₃≀C₃	Direct product of C₆ and C₃≀C₃	54		C6xC3wrC3	486,210
C₂×C₉.He₃	Direct product of C₂ and C₉.He₃	54	3	C2xC9.He3	486,214
C₂×C₃³⋊C₃²	Direct product of C₂ and C₃³⋊C₃²	54	9	C2xC3^3:C3^2	486,215
C₂×He₃.C₃²	Direct product of C₂ and He₃.C₃²	54	9	C2xHe3.C3^2	486,216
C₂×He₃⋊C₃²	Direct product of C₂ and He₃⋊C₃²	54	9	C2xHe3:C3^2	486,217
C₂×C₃².C₃³	Direct product of C₂ and C₃².C₃³	54	9	C2xC3^2.C3^3	486,218
C₂×C₉.₂He₃	Direct product of C₂ and C₉.₂He₃	54	9	C2xC9.2He3	486,219
C₃²×C₃²⋊C₆	Direct product of C₃² and C₃²⋊C₆	54		C3^2xC3^2:C6	486,222
C₃×S₃×He₃	Direct product of C₃, S₃ and He₃	54		C3xS3xHe3	486,223
C₃²×C₉⋊C₆	Direct product of C₃² and C₉⋊C₆	54		C3^2xC9:C6	486,224
C₃×S₃×3_-¹⁺²	Direct product of C₃, S₃ and 3_-¹⁺²	54		C3xS3xES-(3,1)	486,225
S₃×C₉○He₃	Direct product of S₃ and C₉○He₃	54	6	S3xC9oHe3	486,226
C₃²×C₉⋊S₃	Direct product of C₃² and C₉⋊S₃	54		C3^2xC9:S3	486,227
C₃⋊S₃×C₃×C₉	Direct product of C₃×C₉ and C₃⋊S₃	54		C3:S3xC3xC9	486,228
C₃×He₃⋊₄S₃	Direct product of C₃ and He₃⋊₄S₃	54		C3xHe3:4S3	486,229
C₃⋊S₃×He₃	Direct product of C₃⋊S₃ and He₃	54		C3:S3xHe3	486,231
C₃×C₃³.S₃	Direct product of C₃ and C₃³.S₃	54		C3xC3^3.S3	486,232
C₃⋊S₃×3_-¹⁺²	Direct product of C₃⋊S₃ and 3_-¹⁺²	54		C3:S3xES-(3,1)	486,233
C₃×He₃.₄S₃	Direct product of C₃ and He₃.₄S₃	54	6	C3xHe3.4S3	486,234
C₃×He₃⋊₅S₃	Direct product of C₃ and He₃⋊₅S₃	54		C3xHe3:5S3	486,243
C₉○He₃⋊₄S₃	2^nd semidirect product of C₉○He₃ and S₃ acting via S₃/C₃=C₂	54	6	C9oHe3:4S3	486,246
C₃⁴⋊₁₃S₃	13^rd semidirect product of C₃⁴ and S₃ acting faithfully	54		C3^4:13S3	486,248
C₂×3₊¹⁺⁴	Direct product of C₂ and 3₊¹⁺⁴	54	9	C2xES+(3,2)	486,254
C₂×3_-¹⁺⁴	Direct product of C₂ and 3_-¹⁺⁴	54	9	C2xES-(3,2)	486,255
C₃⋊S₃×C₃³	Direct product of C₃³ and C₃⋊S₃	54		C3:S3xC3^3	486,257
C₃²×C₃³⋊C₂	Direct product of C₃² and C₃³⋊C₂	54		C3^2xC3^3:C2	486,258

On 55 points

Groups of order 55

		d	ρ	Label	ID
C₅₅	Cyclic group	55	1	C55	55,2

Groups of order 110

		d	ρ	Label	ID
D₅×C₁₁	Direct product of C₁₁ and D₅	55	2	D5xC11	110,3
C₅×D₁₁	Direct product of C₅ and D₁₁	55	2	C5xD11	110,4
D₅₅	Dihedral group	55	2+	D55	110,5

Groups of order 220

		d	ρ	Label	ID
C₁₁×F₅	Direct product of C₁₁ and F₅	55	4	C11xF5	220,9
C₁₁⋊F₅	The semidirect product of C₁₁ and F₅ acting via F₅/D₅=C₂	55	4	C11:F5	220,10
D₅×D₁₁	Direct product of D₅ and D₁₁	55	4+	D5xD11	220,11

Groups of order 275

		d	ρ	Label	ID
C₅×C₁₁⋊C₅	Direct product of C₅ and C₁₁⋊C₅	55	5	C5xC11:C5	275,3

Groups of order 440

		d	ρ	Label	ID
F₅×D₁₁	Direct product of F₅ and D₁₁	55	8+	F5xD11	440,43

On 56 points

Groups of order 56

		d	ρ	Label	ID
C₇⋊C₈	The semidirect product of C₇ and C₈ acting via C₈/C₄=C₂	56	2	C7:C8	56,1
C₅₆	Cyclic group	56	1	C56	56,2
Dic₁₄	Dicyclic group; = C₇ ⋊Q₈	56	2-	Dic14	56,3
C₂×Dic₇	Direct product of C₂ and Dic₇	56		C2xDic7	56,6
C₂×C₂₈	Abelian group of type [2,28]	56		C2xC28	56,8
C₇×Q₈	Direct product of C₇ and Q₈	56	2	C7xQ8	56,10
C₂²×C₁₄	Abelian group of type [2,2,14]	56		C2^2xC14	56,13

Groups of order 112

		d	ρ	Label	ID
C₈×D₇	Direct product of C₈ and D₇	56	2	C8xD7	112,3
C₈⋊D₇	3^rd semidirect product of C₈ and D₇ acting via D₇/C₇=C₂	56	2	C8:D7	112,4
C₅₆⋊C₂	2^nd semidirect product of C₅₆ and C₂ acting faithfully	56	2	C56:C2	112,5
D₅₆	Dihedral group	56	2+	D56	112,6
C₄.Dic₇	The non-split extension by C₄ of Dic₇ acting via Dic₇/C₁₄=C₂	56	2	C4.Dic7	112,9
D₁₄⋊C₄	The semidirect product of D₁₄ and C₄ acting via C₄/C₂=C₂	56		D14:C4	112,13
D₄⋊D₇	The semidirect product of D₄ and D₇ acting via D₇/C₇=C₂	56	4+	D4:D7	112,14
D₄.D₇	The non-split extension by D₄ of D₇ acting via D₇/C₇=C₂	56	4-	D4.D7	112,15
Q₈⋊D₇	The semidirect product of Q₈ and D₇ acting via D₇/C₇=C₂	56	4+	Q8:D7	112,16
C₂³.D₇	The non-split extension by C₂³ of D₇ acting via D₇/C₇=C₂	56		C2^3.D7	112,18
C₇×C₂²⋊C₄	Direct product of C₇ and C₂²⋊C₄	56		C7xC2^2:C4	112,20
C₇×M₄(2)	Direct product of C₇ and M₄(2)	56	2	C7xM4(2)	112,23
C₇×D₈	Direct product of C₇ and D₈	56	2	C7xD8	112,24
C₇×SD₁₆	Direct product of C₇ and SD₁₆	56	2	C7xSD16	112,25
C₂×C₄×D₇	Direct product of C₂×C₄ and D₇	56		C2xC4xD7	112,28
C₂×D₂₈	Direct product of C₂ and D₂₈	56		C2xD28	112,29
C₄○D₂₈	Central product of C₄ and D₂₈	56	2	C4oD28	112,30
D₄⋊₂D₇	The semidirect product of D₄ and D₇ acting through Inn(D₄)	56	4-	D4:2D7	112,32
Q₈×D₇	Direct product of Q₈ and D₇	56	4-	Q8xD7	112,33
Q₈⋊₂D₇	The semidirect product of Q₈ and D₇ acting through Inn(Q₈)	56	4+	Q8:2D7	112,34
C₂×C₇⋊D₄	Direct product of C₂ and C₇⋊D₄	56		C2xC7:D4	112,36
D₄×C₁₄	Direct product of C₁₄ and D₄	56		D4xC14	112,38
C₇×C₄○D₄	Direct product of C₇ and C₄○D₄	56	2	C7xC4oD4	112,40
C₂³×D₇	Direct product of C₂³ and D₇	56		C2^3xD7	112,42

Groups of order 168

		d	ρ	Label	ID
C₇⋊C₂₄	The semidirect product of C₇ and C₂₄ acting via C₂₄/C₄=C₆	56	6	C7:C24	168,1
C₈×C₇⋊C₃	Direct product of C₈ and C₇⋊C₃	56	3	C8xC7:C3	168,2
C₄.F₇	The non-split extension by C₄ of F₇ acting via F₇/C₇⋊C₃=C₂	56	6-	C4.F7	168,7
C₂×C₇⋊C₁₂	Direct product of C₂ and C₇⋊C₁₂	56		C2xC7:C12	168,10
C₂×C₄×C₇⋊C₃	Direct product of C₂×C₄ and C₇⋊C₃	56		C2xC4xC7:C3	168,19
Q₈×C₇⋊C₃	Direct product of Q₈ and C₇⋊C₃	56	6	Q8xC7:C3	168,21
C₇×SL₂(𝔽₃)	Direct product of C₇ and SL₂(𝔽₃)	56	2	C7xSL(2,3)	168,22
C₁₄.A₄	The non-split extension by C₁₄ of A₄ acting via A₄/C₂²=C₃	56	6	C14.A4	168,23
C₂³×C₇⋊C₃	Direct product of C₂³ and C₇⋊C₃	56		C2^3xC7:C3	168,51

Groups of order 224

		d	ρ	Label	ID
Dic₁₄⋊C₄	1^st semidirect product of Dic₁₄ and C₄ acting via C₄/C₂=C₂	56	2	Dic14:C4	224,11
C₂³.₁D₁₄	1^st non-split extension by C₂³ of D₁₄ acting via D₁₄/C₇=C₂²	56	4	C2^3.1D14	224,12
C₂₈.₄₆D₄	3^rd non-split extension by C₂₈ of D₄ acting via D₄/C₂²=C₂	56	4+	C28.46D4	224,29
D₂₈⋊₄C₄	4^th semidirect product of D₂₈ and C₄ acting via C₄/C₂=C₂	56	4	D28:4C4	224,31
C₂₈.D₄	8^th non-split extension by C₂₈ of D₄ acting via D₄/C₂=C₂²	56	4	C28.D4	224,39
C₂³⋊Dic₇	The semidirect product of C₂³ and Dic₇ acting via Dic₇/C₇=C₄	56	4	C2^3:Dic7	224,40
D₄⋊₂Dic₇	2^nd semidirect product of D₄ and Dic₇ acting via Dic₇/C₁₄=C₂	56	4	D4:2Dic7	224,43
C₇×C₂³⋊C₄	Direct product of C₇ and C₂³⋊C₄	56	4	C7xC2^3:C4	224,48
C₇×C₄.D₄	Direct product of C₇ and C₄.D₄	56	4	C7xC4.D4	224,49
C₇×C₄≀C₂	Direct product of C₇ and C₄≀C₂	56	2	C7xC4wrC2	224,53
D₇×C₂²⋊C₄	Direct product of D₇ and C₂²⋊C₄	56		D7xC2^2:C4	224,75
C₂²⋊D₂₈	The semidirect product of C₂² and D₂₈ acting via D₂₈/D₁₄=C₂	56		C2^2:D28	224,77
D₇×M₄(2)	Direct product of D₇ and M₄(2)	56	4	D7xM4(2)	224,101
C₈⋊D₁₄	1^st semidirect product of C₈ and D₁₄ acting via D₁₄/C₇=C₂²	56	4+	C8:D14	224,103
D₇×D₈	Direct product of D₇ and D₈	56	4+	D7xD8	224,105
D₈⋊D₇	2^nd semidirect product of D₈ and D₇ acting via D₇/C₇=C₂	56	4	D8:D7	224,106
D₇×SD₁₆	Direct product of D₇ and SD₁₆	56	4	D7xSD16	224,108
D₅₆⋊C₂	6^th semidirect product of D₅₆ and C₂ acting faithfully	56	4+	D56:C2	224,109
D₄.D₁₄	1^st non-split extension by D₄ of D₁₄ acting via D₁₄/C₁₄=C₂	56	4	D4.D14	224,127
C₂³⋊D₁₄	1^st semidirect product of C₂³ and D₁₄ acting via D₁₄/C₇=C₂²	56		C2^3:D14	224,132
D₄⋊D₁₄	2^nd semidirect product of D₄ and D₁₄ acting via D₁₄/C₁₄=C₂	56	4+	D4:D14	224,144
C₂⁴⋊D₇	1^st semidirect product of C₂⁴ and D₇ acting via D₇/C₇=C₂	56		C2^4:D7	224,148
C₇×C₂²≀C₂	Direct product of C₇ and C₂²≀C₂	56		C7xC2^2wrC2	224,155
C₇×C₈⋊C₂²	Direct product of C₇ and C₈⋊C₂²	56	4	C7xC8:C2^2	224,171
C₂×D₄×D₇	Direct product of C₂, D₄ and D₇	56		C2xD4xD7	224,178
D₄⋊₆D₁₄	2^nd semidirect product of D₄ and D₁₄ acting through Inn(D₄)	56	4	D4:6D14	224,180
D₇×C₄○D₄	Direct product of D₇ and C₄○D₄	56	4	D7xC4oD4	224,184
D₄⋊₈D₁₄	4^th semidirect product of D₄ and D₁₄ acting through Inn(D₄)	56	4+	D4:8D14	224,185
C₇×2₊¹⁺⁴	Direct product of C₇ and 2₊¹⁺⁴	56	4	C7xES+(2,2)	224,193

Groups of order 336

		d	ρ	Label	ID
C₈×F₇	Direct product of C₈ and F₇	56	6	C8xF7	336,7
C₈⋊F₇	3^rd semidirect product of C₈ and F₇ acting via F₇/C₇⋊C₃=C₂	56	6	C8:F7	336,8
C₅₆⋊C₆	2^nd semidirect product of C₅₆ and C₆ acting faithfully	56	6	C56:C6	336,9
D₅₆⋊C₃	The semidirect product of D₅₆ and C₃ acting faithfully	56	6+	D56:C3	336,10
C₂₈.C₁₂	1^st non-split extension by C₂₈ of C₁₂ acting via C₁₂/C₂=C₆	56	6	C28.C12	336,13
D₁₄⋊C₁₂	The semidirect product of D₁₄ and C₁₂ acting via C₁₂/C₂=C₆	56		D14:C12	336,17
D₄⋊F₇	The semidirect product of D₄ and F₇ acting via F₇/C₇⋊C₃=C₂	56	12+	D4:F7	336,18
D₄.F₇	The non-split extension by D₄ of F₇ acting via F₇/C₇⋊C₃=C₂	56	12-	D4.F7	336,19
Q₈⋊₂F₇	The semidirect product of Q₈ and F₇ acting via F₇/C₇⋊C₃=C₂	56	12+	Q8:2F7	336,20
C₂³.₂F₇	The non-split extension by C₂³ of F₇ acting via F₇/C₇⋊C₃=C₂	56		C2^3.2F7	336,22
C₂²⋊C₄×C₇⋊C₃	Direct product of C₂²⋊C₄ and C₇⋊C₃	56		C2^2:C4xC7:C3	336,49
M₄(2)×C₇⋊C₃	Direct product of M₄(2) and C₇⋊C₃	56	6	M4(2)xC7:C3	336,52
D₈×C₇⋊C₃	Direct product of D₈ and C₇⋊C₃	56	6	D8xC7:C3	336,53
SD₁₆×C₇⋊C₃	Direct product of SD₁₆ and C₇⋊C₃	56	6	SD16xC7:C3	336,54
C₇×GL₂(𝔽₃)	Direct product of C₇ and GL₂(𝔽₃)	56	2	C7xGL(2,3)	336,116
Q₈⋊D₂₁	The semidirect product of Q₈ and D₂₁ acting via D₂₁/C₇=S₃	56	4+	Q8:D21	336,119
C₂×C₄×F₇	Direct product of C₂×C₄ and F₇	56		C2xC4xF7	336,122
C₂×C₄⋊F₇	Direct product of C₂ and C₄⋊F₇	56		C2xC4:F7	336,123
D₂₈⋊₆C₆	2^nd semidirect product of D₂₈ and C₆ acting via C₆/C₂=C₃	56	6	D28:6C6	336,124
D₄⋊₂F₇	The semidirect product of D₄ and F₇ acting through Inn(D₄)	56	12-	D4:2F7	336,126
Q₈×F₇	Direct product of Q₈ and F₇	56	12-	Q8xF7	336,127
Q₈⋊₃F₇	The semidirect product of Q₈ and F₇ acting through Inn(Q₈)	56	12+	Q8:3F7	336,128
C₂×Dic₇⋊C₆	Direct product of C₂ and Dic₇⋊C₆	56		C2xDic7:C6	336,130
D₇×SL₂(𝔽₃)	Direct product of D₇ and SL₂(𝔽₃)	56	4-	D7xSL(2,3)	336,132
Q₈⋊F₇	The semidirect product of Q₈ and F₇ acting via F₇/D₇=C₃	56	12-	Q8:F7	336,135
C₂×D₄×C₇⋊C₃	Direct product of C₂, D₄ and C₇⋊C₃	56		C2xD4xC7:C3	336,165
C₄○D₄×C₇⋊C₃	Direct product of C₄○D₄ and C₇⋊C₃	56	6	C4oD4xC7:C3	336,167
C₂³×F₇	Direct product of C₂³ and F₇	56		C2^3xF7	336,216

Groups of order 392

		d	ρ	Label	ID
C₇×C₇⋊C₈	Direct product of C₇ and C₇⋊C₈	56	2	C7xC7:C8	392,14
C₇²⋊₂C₈	The semidirect product of C₇² and C₈ acting via C₈/C₂=C₄	56	4-	C7^2:2C8	392,17
D₇×Dic₇	Direct product of D₇ and Dic₇	56	4-	D7xDic7	392,18
C₇²⋊₂D₄	1^st semidirect product of C₇² and D₄ acting via D₄/C₂=C₂²	56	4-	C7^2:2D4	392,20
C₇²⋊₂Q₈	The semidirect product of C₇² and Q₈ acting via Q₈/C₂=C₂²	56	4-	C7^2:2Q8	392,22
C₇×Dic₁₄	Direct product of C₇ and Dic₁₄	56	2	C7xDic14	392,23
D₇×C₂₈	Direct product of C₂₈ and D₇	56	2	D7xC28	392,24
C₇×D₂₈	Direct product of C₇ and D₂₈	56	2	C7xD28	392,25
C₁₄×Dic₇	Direct product of C₁₄ and Dic₇	56		C14xDic7	392,26
C₇×F₈	Direct product of C₇ and F₈	56	7	C7xF8	392,39
D₇×C₂×C₁₄	Direct product of C₂×C₁₄ and D₇	56		D7xC2xC14	392,42

Groups of order 448

		d	ρ	Label	ID
C₇⋊C₂≀C₄	The semidirect product of C₇ and C₂≀C₄ acting via C₂≀C₄/C₂³⋊C₄=C₂	56	8+	C7:C2wrC4	448,28
C₂³.₂D₂₈	2^nd non-split extension by C₂³ of D₂₈ acting via D₂₈/C₇=D₄	56	8+	C2^3.2D28	448,31
C₂³.₃D₂₈	3^rd non-split extension by C₂³ of D₂₈ acting via D₂₈/C₇=D₄	56	8+	C2^3.3D28	448,32
C₂⁴⋊Dic₇	1^st semidirect product of C₂⁴ and Dic₇ acting via Dic₇/C₇=C₄	56	4	C2^4:Dic7	448,93
C₄²⋊₃Dic₇	3^rd semidirect product of C₄² and Dic₇ acting via Dic₇/C₇=C₄	56	4	C4^2:3Dic7	448,102
C₇×C₂≀C₄	Direct product of C₇ and C₂≀C₄	56	4	C7xC2wrC4	448,155
C₇×C₄²⋊C₄	Direct product of C₇ and C₄²⋊C₄	56	4	C7xC4^2:C4	448,157
C₂³.F₈	2^nd non-split extension by C₂³ of F₈ acting via F₈/C₂³=C₇	56	14	C2^3.F8	448,179
C₂³⋊D₂₈	The semidirect product of C₂³ and D₂₈ acting via D₂₈/C₇=D₄	56	8+	C2^3:D28	448,275
D₇×C₂³⋊C₄	Direct product of D₇ and C₂³⋊C₄	56	8+	D7xC2^3:C4	448,277
D₇×C₄.D₄	Direct product of D₇ and C₄.D₄	56	8+	D7xC4.D4	448,278
D₂₈⋊₁D₄	1^st semidirect product of D₂₈ and D₄ acting via D₄/C₂=C₂²	56	8+	D28:1D4	448,281
D₇×C₄≀C₂	Direct product of D₇ and C₄≀C₂	56	4	D7xC4wrC2	448,354
D₄⋊₄D₂₈	3^rd semidirect product of D₄ and D₂₈ acting via D₂₈/D₁₄=C₂	56	4+	D4:4D28	448,356
C₂⁴⋊D₁₄	1^st semidirect product of C₂⁴ and D₁₄ acting via D₁₄/C₇=C₂²	56	4	C2^4:D14	448,566
D₂₈⋊₅D₄	5^th semidirect product of D₂₈ and D₄ acting via D₄/C₂=C₂²	56	4	D28:5D4	448,611
D₂₈⋊₁₈D₄	6^th semidirect product of D₂₈ and D₄ acting via D₄/C₂²=C₂	56	8+	D28:18D4	448,732
2₊¹⁺⁴⋊D₇	1^st semidirect product of 2₊¹⁺⁴ and D₇ acting via D₇/C₇=C₂	56	8+	ES+(2,2):D7	448,775
2₊¹⁺⁴⋊₂D₇	2^nd semidirect product of 2₊¹⁺⁴ and D₇ acting via D₇/C₇=C₂	56	8+	ES+(2,2):2D7	448,778
C₇×D₄⋊₄D₄	Direct product of C₇ and D₄⋊₄D₄	56	4	C7xD4:4D4	448,861
C₇×C₂≀C₂²	Direct product of C₇ and C₂≀C₂²	56	4	C7xC2wrC2^2	448,865
C₈×F₈	Direct product of C₈ and F₈	56	7	C8xF8	448,919
D₇×C₂²≀C₂	Direct product of D₇ and C₂²≀C₂	56		D7xC2^2wrC2	448,1041
D₇×C₈⋊C₂²	Direct product of D₇ and C₈⋊C₂²	56	8+	D7xC8:C2^2	448,1225
C₂×C₄×F₈	Direct product of C₂×C₄ and F₈	56		C2xC4xF8	448,1362
Q₈×F₈	Direct product of Q₈ and F₈	56	14-	Q8xF8	448,1364
D₇×2₊¹⁺⁴	Direct product of D₇ and 2₊¹⁺⁴	56	8+	D7xES+(2,2)	448,1379
C₂³×F₈	Direct product of C₂³ and F₈	56		C2^3xF8	448,1392

On 57 points

Groups of order 57

		d	ρ	Label	ID
C₅₇	Cyclic group	57	1	C57	57,2

Groups of order 114

		d	ρ	Label	ID
S₃×C₁₉	Direct product of C₁₉ and S₃	57	2	S3xC19	114,3
C₃×D₁₉	Direct product of C₃ and D₁₉	57	2	C3xD19	114,4
D₅₇	Dihedral group	57	2+	D57	114,5

Groups of order 171

		d	ρ	Label	ID
C₃×C₁₉⋊C₃	Direct product of C₃ and C₁₉⋊C₃	57	3	C3xC19:C3	171,4

Groups of order 228

		d	ρ	Label	ID
S₃×D₁₉	Direct product of S₃ and D₁₉	57	4+	S3xD19	228,8

Groups of order 342

		d	ρ	Label	ID
C₃×C₁₉⋊C₆	Direct product of C₃ and C₁₉⋊C₆	57	6	C3xC19:C6	342,9
S₃×C₁₉⋊C₃	Direct product of S₃ and C₁₉⋊C₃	57	6	S3xC19:C3	342,10
D₅₇⋊C₃	The semidirect product of D₅₇ and C₃ acting faithfully	57	6+	D57:C3	342,11

On 58 points

Groups of order 58

		d	ρ	Label	ID
C₅₈	Cyclic group	58	1	C58	58,2

Groups of order 116

		d	ρ	Label	ID
D₅₈	Dihedral group; = C₂×D₂₉	58	2+	D58	116,4

Groups of order 232

		d	ρ	Label	ID
C₂×C₂₉⋊C₄	Direct product of C₂ and C₂₉⋊C₄	58	4+	C2xC29:C4	232,12

Groups of order 406

		d	ρ	Label	ID
C₂×C₂₉⋊C₇	Direct product of C₂ and C₂₉⋊C₇	58	7	C2xC29:C7	406,2

On 59 points

Groups of order 59

		d	ρ	Label	ID
C₅₉	Cyclic group	59	1	C59	59,1

Groups of order 118

		d	ρ	Label	ID
D₅₉	Dihedral group	59	2+	D59	118,1

On 60 points

Groups of order 60

		d	ρ	Label	ID
C₅×Dic₃	Direct product of C₅ and Dic₃	60	2	C5xDic3	60,1
C₃×Dic₅	Direct product of C₃ and Dic₅	60	2	C3xDic5	60,2
Dic₁₅	Dicyclic group; = C₃ ⋊Dic₅	60	2-	Dic15	60,3
C₆₀	Cyclic group	60	1	C60	60,4
C₂×C₃₀	Abelian group of type [2,30]	60		C2xC30	60,13

Groups of order 120

		d	ρ	Label	ID
D₅×Dic₃	Direct product of D₅ and Dic₃	60	4-	D5xDic3	120,8
S₃×Dic₅	Direct product of S₃ and Dic₅	60	4-	S3xDic5	120,9
D₃₀.C₂	The non-split extension by D₃₀ of C₂ acting faithfully	60	4+	D30.C2	120,10
C₁₅⋊D₄	1^st semidirect product of C₁₅ and D₄ acting via D₄/C₂=C₂²	60	4-	C15:D4	120,11
C₃⋊D₂₀	The semidirect product of C₃ and D₂₀ acting via D₂₀/D₁₀=C₂	60	4+	C3:D20	120,12
C₅⋊D₁₂	The semidirect product of C₅ and D₁₂ acting via D₁₂/D₆=C₂	60	4+	C5:D12	120,13
D₅×C₁₂	Direct product of C₁₂ and D₅	60	2	D5xC12	120,17
C₃×D₂₀	Direct product of C₃ and D₂₀	60	2	C3xD20	120,18
C₃×C₅⋊D₄	Direct product of C₃ and C₅⋊D₄	60	2	C3xC5:D4	120,20
S₃×C₂₀	Direct product of C₂₀ and S₃	60	2	S3xC20	120,22
C₅×D₁₂	Direct product of C₅ and D₁₂	60	2	C5xD12	120,23
C₅×C₃⋊D₄	Direct product of C₅ and C₃⋊D₄	60	2	C5xC3:D4	120,25
C₄×D₁₅	Direct product of C₄ and D₁₅	60	2	C4xD15	120,27
D₆₀	Dihedral group	60	2+	D60	120,28
C₁₅⋊₇D₄	1^st semidirect product of C₁₅ and D₄ acting via D₄/C₂²=C₂	60	2	C15:7D4	120,30
D₄×C₁₅	Direct product of C₁₅ and D₄	60	2	D4xC15	120,32
D₅×C₂×C₆	Direct product of C₂×C₆ and D₅	60		D5xC2xC6	120,44
S₃×C₂×C₁₀	Direct product of C₂×C₁₀ and S₃	60		S3xC2xC10	120,45
C₂²×D₁₅	Direct product of C₂² and D₁₅	60		C2^2xD15	120,46

Groups of order 180

		d	ρ	Label	ID
Dic₃×C₁₅	Direct product of C₁₅ and Dic₃	60	2	Dic3xC15	180,14
C₃×Dic₁₅	Direct product of C₃ and Dic₁₅	60	2	C3xDic15	180,15
A₄×C₁₅	Direct product of C₁₅ and A₄	60	3	A4xC15	180,31
S₃×C₃₀	Direct product of C₃₀ and S₃	60	2	S3xC30	180,33
C₆×D₁₅	Direct product of C₆ and D₁₅	60	2	C6xD15	180,34

Groups of order 240

		d	ρ	Label	ID
C₅×C₄²⋊C₃	Direct product of C₅ and C₄²⋊C₃	60	3	C5xC4^2:C3	240,32
Dic₃×F₅	Direct product of Dic₃ and F₅	60	8-	Dic3xF5	240,95
D₆⋊F₅	The semidirect product of D₆ and F₅ acting via F₅/D₅=C₂	60	8+	D6:F5	240,96
Dic₃⋊F₅	The semidirect product of Dic₃ and F₅ acting via F₅/D₅=C₂	60	8-	Dic3:F5	240,97
C₅×A₄⋊C₄	Direct product of C₅ and A₄⋊C₄	60	3	C5xA4:C4	240,104
A₄⋊Dic₅	The semidirect product of A₄ and Dic₅ acting via Dic₅/C₁₀=C₂	60	6-	A4:Dic5	240,107
A₄×Dic₅	Direct product of A₄ and Dic₅	60	6-	A4xDic5	240,110
C₁₂×F₅	Direct product of C₁₂ and F₅	60	4	C12xF5	240,113
C₃×C₄⋊F₅	Direct product of C₃ and C₄⋊F₅	60	4	C3xC4:F5	240,114
C₃×C₂²⋊F₅	Direct product of C₃ and C₂²⋊F₅	60	4	C3xC2^2:F5	240,117
C₄×C₃⋊F₅	Direct product of C₄ and C₃⋊F₅	60	4	C4xC3:F5	240,120
C₆₀⋊C₄	1^st semidirect product of C₆₀ and C₄ acting faithfully	60	4	C60:C4	240,121
D₁₀.D₆	6^th non-split extension by D₁₀ of D₆ acting via D₆/C₆=C₂	60	4	D10.D6	240,124
C₄×S₃×D₅	Direct product of C₄, S₃ and D₅	60	4	C4xS3xD5	240,135
D₅×D₁₂	Direct product of D₅ and D₁₂	60	4+	D5xD12	240,136
S₃×D₂₀	Direct product of S₃ and D₂₀	60	4+	S3xD20	240,137
C₂₀⋊D₆	2^nd semidirect product of C₂₀ and D₆ acting via D₆/C₃=C₂²	60	4	C20:D6	240,138
D₅×C₃⋊D₄	Direct product of D₅ and C₃⋊D₄	60	4	D5xC3:D4	240,149
S₃×C₅⋊D₄	Direct product of S₃ and C₅⋊D₄	60	4	S3xC5:D4	240,150
D₁₀⋊D₆	4^th semidirect product of D₁₀ and D₆ acting via D₆/S₃=C₂	60	4+	D10:D6	240,151
A₄×C₂₀	Direct product of C₂₀ and A₄	60	3	A4xC20	240,152
C₃×D₄×D₅	Direct product of C₃, D₄ and D₅	60	4	C3xD4xD5	240,159
C₅×S₃×D₄	Direct product of C₅, S₃ and D₄	60	4	C5xS3xD4	240,169
D₄×D₁₅	Direct product of D₄ and D₁₅	60	4+	D4xD15	240,179
C₂×C₆×F₅	Direct product of C₂×C₆ and F₅	60		C2xC6xF5	240,200
C₂²×C₃⋊F₅	Direct product of C₂² and C₃⋊F₅	60		C2^2xC3:F5	240,201
C₂²×S₃×D₅	Direct product of C₂², S₃ and D₅	60		C2^2xS3xD5	240,202
A₄×C₂×C₁₀	Direct product of C₂×C₁₀ and A₄	60		A4xC2xC10	240,203
C₅×C₂²⋊A₄	Direct product of C₅ and C₂²⋊A₄	60		C5xC2^2:A4	240,204

Groups of order 300

		d	ρ	Label	ID
C₅²⋊₂Dic₃	The semidirect product of C₅² and Dic₃ acting via Dic₃/C₂=S₃	60	3	C5^2:2Dic3	300,13
C₅²⋊₂C₁₂	The semidirect product of C₅² and C₁₂ acting via C₁₂/C₂=C₆	60	6-	C5^2:2C12	300,14
C₄×C₅²⋊C₃	Direct product of C₄ and C₅²⋊C₃	60	3	C4xC5^2:C3	300,15
C₁₅×Dic₅	Direct product of C₁₅ and Dic₅	60	2	C15xDic5	300,16
C₅×Dic₁₅	Direct product of C₅ and Dic₁₅	60	2	C5xDic15	300,19
C₁₅×F₅	Direct product of C₁₅ and F₅	60	4	C15xF5	300,28
C₃×D₅.D₅	Direct product of C₃ and D₅.D₅	60	4	C3xD5.D5	300,29
C₅×C₃⋊F₅	Direct product of C₅ and C₃⋊F₅	60	4	C5xC3:F5	300,32
D₅.D₁₅	The non-split extension by D₅ of D₁₅ acting via D₁₅/C₁₅=C₂	60	4	D5.D15	300,33
C₂²×C₅²⋊C₃	Direct product of C₂² and C₅²⋊C₃	60		C2^2xC5^2:C3	300,41
D₅×C₃₀	Direct product of C₃₀ and D₅	60	2	D5xC30	300,44
C₁₀×D₁₅	Direct product of C₁₀ and D₁₅	60	2	C10xD15	300,47

Groups of order 360

		d	ρ	Label	ID
C₃×D₅×Dic₃	Direct product of C₃, D₅ and Dic₃	60	4	C3xD5xDic3	360,58
C₃×C₁₅⋊D₄	Direct product of C₃ and C₁₅⋊D₄	60	4	C3xC15:D4	360,61
C₃×C₃⋊D₂₀	Direct product of C₃ and C₃⋊D₂₀	60	4	C3xC3:D20	360,62
C₅×C₆.D₆	Direct product of C₅ and C₆.D₆	60	4	C5xC6.D6	360,73
C₅×C₃⋊D₁₂	Direct product of C₅ and C₃⋊D₁₂	60	4	C5xC3:D12	360,75
C₆.D₃₀	3^rd non-split extension by C₆ of D₃₀ acting via D₃₀/D₁₅=C₂	60	4+	C6.D30	360,79
C₃⋊D₆₀	The semidirect product of C₃ and D₆₀ acting via D₆₀/D₃₀=C₂	60	4+	C3:D60	360,81
D₆⋊₂D₁₅	2^nd semidirect product of D₆ and D₁₅ acting via D₁₅/C₁₅=C₂	60	4+	D6:2D15	360,82
Dic₁₅⋊S₃	3^rd semidirect product of Dic₁₅ and S₃ acting via S₃/C₃=C₂	60	4	Dic15:S3	360,85
D₃₀⋊S₃	3^rd semidirect product of D₃₀ and S₃ acting via S₃/C₃=C₂	60	4	D30:S3	360,86
C₁₅×C₃⋊D₄	Direct product of C₁₅ and C₃⋊D₄	60	2	C15xC3:D4	360,99
C₃×C₁₅⋊₇D₄	Direct product of C₃ and C₁₅⋊₇D₄	60	2	C3xC15:7D4	360,104
C₁₅×S₄	Direct product of C₁₅ and S₄	60	3	C15xS4	360,138
C₃×C₅⋊S₄	Direct product of C₃ and C₅⋊S₄	60	6	C3xC5:S4	360,139
C₅×C₃⋊S₄	Direct product of C₅ and C₃⋊S₄	60	6	C5xC3:S4	360,140
A₄⋊D₁₅	The semidirect product of A₄ and D₁₅ acting via D₁₅/C₁₅=C₂	60	6+	A4:D15	360,141
C₃×D₅×A₄	Direct product of C₃, D₅ and A₄	60	6	C3xD5xA4	360,142
C₅×S₃×A₄	Direct product of C₅, S₃ and A₄	60	6	C5xS3xA4	360,143
A₄×D₁₅	Direct product of A₄ and D₁₅	60	6+	A4xD15	360,144
C₆×C₃⋊F₅	Direct product of C₆ and C₃⋊F₅	60	4	C6xC3:F5	360,146
C₁₀×C₃²⋊C₄	Direct product of C₁₀ and C₃²⋊C₄	60	4	C10xC3^2:C4	360,148
C₂×C₃²⋊Dic₅	Direct product of C₂ and C₃²⋊Dic₅	60	4	C2xC3^2:Dic5	360,149
C₂×C₃²⋊F₅	Direct product of C₂ and C₃²⋊F₅	60	4+	C2xC3^2:F5	360,150
S₃×C₆×D₅	Direct product of C₆, S₃ and D₅	60	4	S3xC6xD5	360,151
S₃²×C₁₀	Direct product of C₁₀, S₃ and S₃	60	4	S3^2xC10	360,153
C₂×S₃×D₁₅	Direct product of C₂, S₃ and D₁₅	60	4+	C2xS3xD15	360,154
C₂×D₁₅⋊S₃	Direct product of C₂ and D₁₅⋊S₃	60	4	C2xD15:S3	360,155

Groups of order 480

		d	ρ	Label	ID
C₅×C₂³.₃A₄	Direct product of C₅ and C₂³.₃A₄	60	6	C5xC2^3.3A4	480,74
C₅×C₄²⋊S₃	Direct product of C₅ and C₄²⋊S₃	60	3	C5xC4^2:S3	480,254
C₄²⋊D₁₅	The semidirect product of C₄² and D₁₅ acting via D₁₅/C₅=S₃	60	6+	C4^2:D15	480,258
C₂₀⋊₄D₄⋊C₃	The semidirect product of C₂₀⋊₄D₄ and C₃ acting faithfully	60	6+	C20:4D4:C3	480,262
D₅×C₄²⋊C₃	Direct product of D₅ and C₄²⋊C₃	60	6	D5xC4^2:C3	480,264
C₁₀×C₄²⋊C₃	Direct product of C₁₀ and C₄²⋊C₃	60	3	C10xC4^2:C3	480,654
C₅×C₂³.A₄	Direct product of C₅ and C₂³.A₄	60	6	C5xC2^3.A4	480,658
Dic₅×S₄	Direct product of Dic₅ and S₄	60	6-	Dic5xS4	480,976
Dic₅⋊₂S₄	The semidirect product of Dic₅ and S₄ acting through Inn(Dic₅)	60	6	Dic5:2S4	480,977
Dic₅⋊S₄	The semidirect product of Dic₅ and S₄ acting via S₄/A₄=C₂	60	6	Dic5:S4	480,978
D₅×A₄⋊C₄	Direct product of D₅ and A₄⋊C₄	60	6	D5xA4:C4	480,979
D₁₀⋊S₄	1^st semidirect product of D₁₀ and S₄ acting via S₄/A₄=C₂	60	6	D10:S4	480,980
A₄⋊D₂₀	The semidirect product of A₄ and D₂₀ acting via D₂₀/D₁₀=C₂	60	6+	A4:D20	480,981
C₄×S₃×F₅	Direct product of C₄, S₃ and F₅	60	8	C4xS3xF5	480,994
F₅×D₁₂	Direct product of F₅ and D₁₂	60	8+	F5xD12	480,995
S₃×C₄⋊F₅	Direct product of S₃ and C₄⋊F₅	60	8	S3xC4:F5	480,996
D₆₀⋊₃C₄	3^rd semidirect product of D₆₀ and C₄ acting faithfully	60	8+	D60:3C4	480,997
F₅×C₃⋊D₄	Direct product of F₅ and C₃⋊D₄	60	8	F5xC3:D4	480,1010
S₃×C₂²⋊F₅	Direct product of S₃ and C₂²⋊F₅	60	8+	S3xC2^2:F5	480,1011
C₃⋊D₄⋊F₅	The semidirect product of C₃⋊D₄ and F₅ acting via F₅/D₅=C₂	60	8	C3:D4:F5	480,1012
C₂₀×S₄	Direct product of C₂₀ and S₄	60	3	C20xS4	480,1014
C₅×C₄⋊S₄	Direct product of C₅ and C₄⋊S₄	60	6	C5xC4:S4	480,1015
C₅×A₄⋊D₄	Direct product of C₅ and A₄⋊D₄	60	6	C5xA4:D4	480,1023
C₄×C₅⋊S₄	Direct product of C₄ and C₅⋊S₄	60	6	C4xC5:S4	480,1025
C₂₀⋊S₄	1^st semidirect product of C₂₀ and S₄ acting via S₄/A₄=C₂	60	6+	C20:S4	480,1026
C₂⁴⋊₂D₁₅	1^st semidirect product of C₂⁴ and D₁₅ acting via D₁₅/C₅=S₃	60	6	C2^4:2D15	480,1034
C₄×D₅×A₄	Direct product of C₄, D₅ and A₄	60	6	C4xD5xA4	480,1036
A₄×D₂₀	Direct product of A₄ and D₂₀	60	6+	A4xD20	480,1037
A₄×C₅⋊D₄	Direct product of A₄ and C₅⋊D₄	60	6	A4xC5:D4	480,1045
C₃×D₄×F₅	Direct product of C₃, D₄ and F₅	60	8	C3xD4xF5	480,1054
D₄×C₃⋊F₅	Direct product of D₄ and C₃⋊F₅	60	8	D4xC3:F5	480,1067
S₃×D₄×D₅	Direct product of S₃, D₄ and D₅	60	8+	S3xD4xD5	480,1097
C₅×D₄×A₄	Direct product of C₅, D₄ and A₄	60	6	C5xD4xA4	480,1127
C₂²×S₃×F₅	Direct product of C₂², S₃ and F₅	60		C2^2xS3xF5	480,1197
C₂×C₁₀×S₄	Direct product of C₂×C₁₀ and S₄	60		C2xC10xS4	480,1198
C₂²×C₅⋊S₄	Direct product of C₂² and C₅⋊S₄	60		C2^2xC5:S4	480,1199
C₂²×D₅×A₄	Direct product of C₂², D₅ and A₄	60		C2^2xD5xA4	480,1202
D₅×C₂²⋊A₄	Direct product of D₅ and C₂²⋊A₄	60		D5xC2^2:A4	480,1203
C₁₀×C₂²⋊A₄	Direct product of C₁₀ and C₂²⋊A₄	60		C10xC2^2:A4	480,1209

On 61 points

Groups of order 61

		d	ρ	Label	ID
C₆₁	Cyclic group	61	1	C61	61,1

Groups of order 122

		d	ρ	Label	ID
D₆₁	Dihedral group	61	2+	D61	122,1

Groups of order 183

		d	ρ	Label	ID
C₆₁⋊C₃	The semidirect product of C₆₁ and C₃ acting faithfully	61	3	C61:C3	183,1

Groups of order 244

		d	ρ	Label	ID
C₆₁⋊C₄	The semidirect product of C₆₁ and C₄ acting faithfully	61	4+	C61:C4	244,3

Groups of order 305

		d	ρ	Label	ID
C₆₁⋊C₅	The semidirect product of C₆₁ and C₅ acting faithfully	61	5	C61:C5	305,1

Groups of order 366

		d	ρ	Label	ID
C₆₁⋊C₆	The semidirect product of C₆₁ and C₆ acting faithfully	61	6+	C61:C6	366,1

On 62 points

Groups of order 62

		d	ρ	Label	ID
C₆₂	Cyclic group	62	1	C62	62,2

Groups of order 124

		d	ρ	Label	ID
D₆₂	Dihedral group; = C₂×D₃₁	62	2+	D62	124,3

Groups of order 186

		d	ρ	Label	ID
C₂×C₃₁⋊C₃	Direct product of C₂ and C₃₁⋊C₃	62	3	C2xC31:C3	186,2

Groups of order 310

		d	ρ	Label	ID
C₂×C₃₁⋊C₅	Direct product of C₂ and C₃₁⋊C₅	62	5	C2xC31:C5	310,2

Groups of order 372

		d	ρ	Label	ID
C₂×C₃₁⋊C₆	Direct product of C₂ and C₃₁⋊C₆	62	6+	C2xC31:C6	372,7

On 63 points

Groups of order 63

		d	ρ	Label	ID
C₇⋊C₉	The semidirect product of C₇ and C₉ acting via C₉/C₃=C₃	63	3	C7:C9	63,1
C₆₃	Cyclic group	63	1	C63	63,2
C₃×C₂₁	Abelian group of type [3,21]	63		C3xC21	63,4

Groups of order 126

		d	ρ	Label	ID
C₇⋊C₁₈	The semidirect product of C₇ and C₁₈ acting via C₁₈/C₃=C₆	63	6	C7:C18	126,1
C₇×D₉	Direct product of C₇ and D₉	63	2	C7xD9	126,3
C₉×D₇	Direct product of C₉ and D₇	63	2	C9xD7	126,4
D₆₃	Dihedral group	63	2+	D63	126,5
C₃²×D₇	Direct product of C₃² and D₇	63		C3^2xD7	126,11
C₇×C₃⋊S₃	Direct product of C₇ and C₃⋊S₃	63		C7xC3:S3	126,14
C₃⋊D₂₁	The semidirect product of C₃ and D₂₁ acting via D₂₁/C₂₁=C₂	63		C3:D21	126,15

Groups of order 189

		d	ρ	Label	ID
C₉×C₇⋊C₃	Direct product of C₉ and C₇⋊C₃	63	3	C9xC7:C3	189,3
C₆₃⋊C₃	2^nd semidirect product of C₆₃ and C₃ acting faithfully	63	3	C63:C3	189,4
C₆₃⋊₃C₃	3^rd semidirect product of C₆₃ and C₃ acting faithfully	63	3	C63:3C3	189,5
C₂₁.C₃²	5^th non-split extension by C₂₁ of C₃² acting via C₃²/C₃=C₃	63	3	C21.C3^2	189,7
C₇⋊He₃	The semidirect product of C₇ and He₃ acting via He₃/C₃²=C₃	63	3	C7:He3	189,8
C₇×He₃	Direct product of C₇ and He₃	63	3	C7xHe3	189,10
C₇×3_-¹⁺²	Direct product of C₇ and 3_-¹⁺²	63	3	C7xES-(3,1)	189,11
C₃²×C₇⋊C₃	Direct product of C₃² and C₇⋊C₃	63		C3^2xC7:C3	189,12

Groups of order 252

		d	ρ	Label	ID
D₇×D₉	Direct product of D₇ and D₉	63	4+	D7xD9	252,8
D₇×C₃⋊S₃	Direct product of D₇ and C₃⋊S₃	63		D7xC3:S3	252,34

Groups of order 378

		d	ρ	Label	ID
C₉×F₇	Direct product of C₉ and F₇	63	6	C9xF7	378,7
C₉⋊₃F₇	1^st semidirect product of C₉ and F₇ acting via F₇/D₇=C₃	63	6	C9:3F7	378,8
C₉⋊₄F₇	2^nd semidirect product of C₉ and F₇ acting via F₇/D₇=C₃	63	6	C9:4F7	378,9
C₃².F₇	The non-split extension by C₃² of F₇ acting via F₇/D₇=C₃	63	6	C3^2.F7	378,11
D₇⋊He₃	The semidirect product of D₇ and He₃ acting via He₃/C₃²=C₃	63	6	D7:He3	378,12
C₆₃⋊C₆	5^th semidirect product of C₆₃ and C₆ acting faithfully	63	6	C63:C6	378,13
C₆₃⋊₆C₆	6^th semidirect product of C₆₃ and C₆ acting faithfully	63	6	C63:6C6	378,14
D₉×C₇⋊C₃	Direct product of D₉ and C₇⋊C₃	63	6	D9xC7:C3	378,15
C₇⋊He₃⋊C₂	3^rd semidirect product of C₇⋊He₃ and C₂ acting faithfully	63	6	C7:He3:C2	378,17
C₉⋊F₇	1^st semidirect product of C₉ and F₇ acting via F₇/C₇=C₆	63	6+	C9:F7	378,18
C₉⋊₂F₇	2^nd semidirect product of C₉ and F₇ acting via F₇/C₇=C₆	63	6+	C9:2F7	378,19
C₉⋊₅F₇	The semidirect product of C₉ and F₇ acting via F₇/C₇⋊C₃=C₂	63	6+	C9:5F7	378,20
C₃²⋊F₇	The semidirect product of C₃² and F₇ acting via F₇/C₇=C₆	63	6+	C3^2:F7	378,22
D₇×He₃	Direct product of D₇ and He₃	63	6	D7xHe3	378,30
D₇×3_-¹⁺²	Direct product of D₇ and 3_-¹⁺²	63	6	D7xES-(3,1)	378,31
C₇×C₃²⋊C₆	Direct product of C₇ and C₃²⋊C₆	63	6	C7xC3^2:C6	378,34
C₇×C₉⋊C₆	Direct product of C₇ and C₉⋊C₆	63	6	C7xC9:C6	378,35
He₃⋊D₇	1^st semidirect product of He₃ and D₇ acting via D₇/C₇=C₂	63	6+	He3:D7	378,38
D₆₃⋊C₃	1^st semidirect product of D₆₃ and C₃ acting faithfully	63	6+	D63:C3	378,39
C₇×He₃⋊C₂	Direct product of C₇ and He₃⋊C₂	63	3	C7xHe3:C2	378,41
C₃²⋊D₂₁	2^nd semidirect product of C₃² and D₂₁ acting via D₂₁/C₇=S₃	63	6	C3^2:D21	378,43
C₃²×F₇	Direct product of C₃² and F₇	63		C3^2xF7	378,47
C₃⋊S₃×C₇⋊C₃	Direct product of C₃⋊S₃ and C₇⋊C₃	63		C3:S3xC7:C3	378,50
C₃²⋊₄F₇	2^nd semidirect product of C₃² and F₇ acting via F₇/C₇⋊C₃=C₂	63		C3^2:4F7	378,51

Groups of order 441

		d	ρ	Label	ID
C₇×C₇⋊C₉	Direct product of C₇ and C₇⋊C₉	63	3	C7xC7:C9	441,5
C₇²⋊₃C₉	3^rd semidirect product of C₇² and C₉ acting via C₉/C₃=C₃	63	3	C7^2:3C9	441,7
C₇⋊C₃×C₂₁	Direct product of C₂₁ and C₇⋊C₃	63	3	C7:C3xC21	441,10
C₃×C₇²⋊₃C₃	Direct product of C₃ and C₇²⋊₃C₃	63	3	C3xC7^2:3C3	441,12

On 64 points

Groups of order 64

		d	ρ	Label	ID
C₆₄	Cyclic group	64	1	C64	64,1
C₈²	Abelian group of type [8,8]	64		C8^2	64,2
C₈⋊C₈	3^rd semidirect product of C₈ and C₈ acting via C₈/C₄=C₂	64		C8:C8	64,3
Q₈⋊C₈	The semidirect product of Q₈ and C₈ acting via C₈/C₄=C₂	64		Q8:C8	64,7
C₄².₂C₂²	2^nd non-split extension by C₄² of C₂² acting faithfully	64		C4^2.2C2^2	64,11
C₄.₁₀D₈	2^nd non-split extension by C₄ of D₈ acting via D₈/D₄=C₂	64		C4.10D8	64,13
C₄.₆Q₁₆	2^nd non-split extension by C₄ of Q₁₆ acting via Q₁₆/Q₈=C₂	64		C4.6Q16	64,14
C₈⋊₂C₈	2^nd semidirect product of C₈ and C₈ acting via C₈/C₄=C₂	64		C8:2C8	64,15
C₈⋊₁C₈	1^st semidirect product of C₈ and C₈ acting via C₈/C₄=C₂	64		C8:1C8	64,16
C₂².₇C₄²	2^nd central extension by C₂² of C₄²	64		C2^2.7C4^2	64,17
C₂².₄Q₁₆	1^st central extension by C₂² of Q₁₆	64		C2^2.4Q16	64,21
C₄×C₁₆	Abelian group of type [4,16]	64		C4xC16	64,26
C₁₆⋊₅C₄	3^rd semidirect product of C₁₆ and C₄ acting via C₄/C₂=C₂	64		C16:5C4	64,27
C₂.Q₃₂	1^st central extension by C₂ of Q₃₂	64		C2.Q32	64,39
C₄⋊C₁₆	The semidirect product of C₄ and C₁₆ acting via C₁₆/C₈=C₂	64		C4:C16	64,44
C₁₆⋊₃C₄	1^st semidirect product of C₁₆ and C₄ acting via C₄/C₂=C₂	64		C16:3C4	64,47
C₁₆⋊₄C₄	2^nd semidirect product of C₁₆ and C₄ acting via C₄/C₂=C₂	64		C16:4C4	64,48
C₂×C₃₂	Abelian group of type [2,32]	64		C2xC32	64,50
Q₆₄	Generalised quaternion group; = C₃₂ .C₂ = Dic₁₆	64	2-	Q64	64,54
C₄³	Abelian group of type [4,4,4]	64		C4^3	64,55
C₂×C₂.C₄²	Direct product of C₂ and C₂.C₄²	64		C2xC2.C4^2	64,56
C₄²⋊₄C₄	1^st semidirect product of C₄² and C₄ acting via C₄/C₂=C₂	64		C4^2:4C4	64,57
C₄×C₄⋊C₄	Direct product of C₄ and C₄⋊C₄	64		C4xC4:C4	64,59
C₄²⋊₈C₄	5^th semidirect product of C₄² and C₄ acting via C₄/C₂=C₂	64		C4^2:8C4	64,63
C₄²⋊₅C₄	2^nd semidirect product of C₄² and C₄ acting via C₄/C₂=C₂	64		C4^2:5C4	64,64
C₄²⋊₉C₄	6^th semidirect product of C₄² and C₄ acting via C₄/C₂=C₂	64		C4^2:9C4	64,65
C₂³.₆₃C₂³	13^rd central extension by C₂³ of C₂³	64		C2^3.63C2^3	64,68
C₂³.₆₅C₂³	15^th central extension by C₂³ of C₂³	64		C2^3.65C2^3	64,70
C₂³.₆₇C₂³	17^th central extension by C₂³ of C₂³	64		C2^3.67C2^3	64,72
C₂³.₇₈C₂³	4^th central stem extension by C₂³ of C₂³	64		C2^3.78C2^3	64,76
C₂³.₈₁C₂³	7^th central stem extension by C₂³ of C₂³	64		C2^3.81C2^3	64,79
C₂³.₈₃C₂³	9^th central stem extension by C₂³ of C₂³	64		C2^3.83C2^3	64,81
C₂³.₈₄C₂³	10^th central stem extension by C₂³ of C₂³	64		C2^3.84C2^3	64,82
C₂×C₄×C₈	Abelian group of type [2,4,8]	64		C2xC4xC8	64,83
C₂×C₈⋊C₄	Direct product of C₂ and C₈⋊C₄	64		C2xC8:C4	64,84
C₂×Q₈⋊C₄	Direct product of C₂ and Q₈⋊C₄	64		C2xQ8:C4	64,96
C₂×C₄⋊C₈	Direct product of C₂ and C₄⋊C₈	64		C2xC4:C8	64,103
C₂×C₄.Q₈	Direct product of C₂ and C₄.Q₈	64		C2xC4.Q8	64,106
C₂×C₂.D₈	Direct product of C₂ and C₂.D₈	64		C2xC2.D8	64,107
C₄×Q₁₆	Direct product of C₄ and Q₁₆	64		C4xQ16	64,120
Q₁₆⋊C₄	3^rd semidirect product of Q₁₆ and C₄ acting via C₄/C₂=C₂	64		Q16:C4	64,122
C₈×Q₈	Direct product of C₈ and Q₈	64		C8xQ8	64,126
C₈⋊₄Q₈	3^rd semidirect product of C₈ and Q₈ acting via Q₈/C₄=C₂	64		C8:4Q8	64,127
C₄⋊₂Q₁₆	The semidirect product of C₄ and Q₁₆ acting via Q₁₆/Q₈=C₂	64		C4:2Q16	64,143
Q₈⋊Q₈	1^st semidirect product of Q₈ and Q₈ acting via Q₈/C₄=C₂	64		Q8:Q8	64,156
C₄.Q₁₆	3^rd non-split extension by C₄ of Q₁₆ acting via Q₁₆/Q₈=C₂	64		C4.Q16	64,158
Q₈.Q₈	The non-split extension by Q₈ of Q₈ acting via Q₈/C₄=C₂	64		Q8.Q8	64,160
C₄.SD₁₆	4^th non-split extension by C₄ of SD₁₆ acting via SD₁₆/C₈=C₂	64		C4.SD16	64,168
C₄².₃₀C₂²	30^th non-split extension by C₄² of C₂² acting faithfully	64		C4^2.30C2^2	64,172
C₄⋊Q₁₆	The semidirect product of C₄ and Q₁₆ acting via Q₁₆/C₈=C₂	64		C4:Q16	64,175
C₈⋊₃Q₈	2^nd semidirect product of C₈ and Q₈ acting via Q₈/C₄=C₂	64		C8:3Q8	64,179
C₈.₅Q₈	4^th non-split extension by C₈ of Q₈ acting via Q₈/C₄=C₂	64		C8.5Q8	64,180
C₈⋊₂Q₈	1^st semidirect product of C₈ and Q₈ acting via Q₈/C₄=C₂	64		C8:2Q8	64,181
C₈⋊Q₈	The semidirect product of C₈ and Q₈ acting via Q₈/C₂=C₂²	64		C8:Q8	64,182
C₂²×C₁₆	Abelian group of type [2,2,16]	64		C2^2xC16	64,183
C₂×Q₃₂	Direct product of C₂ and Q₃₂	64		C2xQ32	64,188
C₂²×C₄²	Abelian group of type [2,2,4,4]	64		C2^2xC4^2	64,192
C₂²×C₄⋊C₄	Direct product of C₂² and C₄⋊C₄	64		C2^2xC4:C4	64,194
C₂×C₄×Q₈	Direct product of C₂×C₄ and Q₈	64		C2xC4xQ8	64,197
C₂×C₄².C₂	Direct product of C₂ and C₄².C₂	64		C2xC4^2.C2	64,208
C₂×C₄⋊Q₈	Direct product of C₂ and C₄⋊Q₈	64		C2xC4:Q8	64,212
Q₈⋊₃Q₈	The semidirect product of Q₈ and Q₈ acting through Inn(Q₈)	64		Q8:3Q8	64,238
Q₈²	Direct product of Q₈ and Q₈	64		Q8^2	64,239
C₂².₅₈C₂⁴	44^th central stem extension by C₂² of C₂⁴	64		C2^2.58C2^4	64,245
C₂³×C₈	Abelian group of type [2,2,2,8]	64		C2^3xC8	64,246
C₂²×Q₁₆	Direct product of C₂² and Q₁₆	64		C2^2xQ16	64,252
C₂⁴×C₄	Abelian group of type [2,2,2,2,4]	64		C2^4xC4	64,260
Q₈×C₂³	Direct product of C₂³ and Q₈	64		Q8xC2^3	64,262
C₂⁶	Elementary abelian group of type [2,2,2,2,2,2]	64		C2^6	64,267

Groups of order 128

		d	ρ	Label	ID
(C₂×C₄).₉₈D₈	1^st non-split extension by C₂×C₄ of D₈ acting via D₈/D₄=C₂	64		(C2xC4).98D8	128,2
C₄².₂₀D₄	2^nd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.20D4	128,7
M₄(2)⋊C₈	2^nd semidirect product of M₄(2) and C₈ acting via C₈/C₄=C₂	64		M4(2):C8	128,10
C₂³.₁₉C₄²	1^st non-split extension by C₂³ of C₄² acting via C₄²/C₂×C₄=C₂	64		C2^3.19C4^2	128,12
C₄².₂Q₈	2^nd non-split extension by C₄² of Q₈ acting via Q₈/C₂=C₂²	64		C4^2.2Q8	128,13
C₄².₃Q₈	3^rd non-split extension by C₄² of Q₈ acting via Q₈/C₂=C₂²	64		C4^2.3Q8	128,15
C₄².₂₃D₄	5^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.23D4	128,19
C₄².₂₅D₄	7^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.25D4	128,22
C₄².₂₆D₄	8^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.26D4	128,23
C₄².₂₇D₄	9^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.27D4	128,24
C₄².₃₈₈D₄	21^st non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.388D4	128,31
C₄².₃₈₉D₄	22^nd non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.389D4	128,33
C₄².₃₇₀D₄	3^rd non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.370D4	128,34
C₄².₃₀D₄	12^nd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.30D4	128,39
C₄².₃₁D₄	13^rd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.31D4	128,40
C₄².₃₂D₄	14^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.32D4	128,41
C₂³.M₄(2)	2^nd non-split extension by C₂³ of M₄(2) acting via M₄(2)/C₄=C₂²	64		C2^3.M4(2)	128,47
C₂².M₅(2)	2^nd non-split extension by C₂² of M₅(2) acting via M₅(2)/C₂×C₈=C₂	64		C2^2.M5(2)	128,54
C₂³.₇M₄(2)	3^rd non-split extension by C₂³ of M₄(2) acting via M₄(2)/C₄=C₂²	64		C2^3.7M4(2)	128,55
D₄⋊C₁₆	The semidirect product of D₄ and C₁₆ acting via C₁₆/C₈=C₂	64		D4:C16	128,61
C₈.₃₁D₈	8^th non-split extension by C₈ of D₈ acting via D₈/D₄=C₂	64		C8.31D8	128,62
C₄.₁₆D₁₆	1^st central extension by C₄ of D₁₆	64		C4.16D16	128,63
D₈⋊C₈	3^rd semidirect product of D₈ and C₈ acting via C₈/C₄=C₂	64		D8:C8	128,65
C₂³.₁₂SD₁₆	2^nd non-split extension by C₂³ of SD₁₆ acting via SD₁₆/C₄=C₂²	64		C2^3.12SD16	128,81
C₂³.₁₃SD₁₆	3^rd non-split extension by C₂³ of SD₁₆ acting via SD₁₆/C₄=C₂²	64		C2^3.13SD16	128,82
C₈.₃₀D₈	7^th non-split extension by C₈ of D₈ acting via D₈/D₄=C₂	64		C8.30D8	128,92
C₄.D₁₆	1^st non-split extension by C₄ of D₁₆ acting via D₁₆/D₈=C₂	64		C4.D16	128,93
M₅(2)⋊C₄	5^th semidirect product of M₅(2) and C₄ acting via C₄/C₂=C₂	64		M5(2):C4	128,109
M₅(2)⋊₇C₄	7^th semidirect product of M₅(2) and C₄ acting via C₄/C₂=C₂	64		M5(2):7C4	128,111
C₈.₈C₄²	2^nd non-split extension by C₈ of C₄² acting via C₄²/C₂×C₄=C₂	64		C8.8C4^2	128,113
C₈.₉C₄²	3^rd non-split extension by C₈ of C₄² acting via C₄²/C₂×C₄=C₂	64		C8.9C4^2	128,114
C₈.₂C₄²	2^nd non-split extension by C₈ of C₄² acting via C₄²/C₂²=C₂²	64		C8.2C4^2	128,119
C₂²⋊C₃₂	The semidirect product of C₂² and C₃₂ acting via C₃₂/C₁₆=C₂	64		C2^2:C32	128,131
D₄.C₁₆	The non-split extension by D₄ of C₁₆ acting via C₁₆/C₈=C₂	64	2	D4.C16	128,133
D₁₆⋊₂C₄	1^st semidirect product of D₁₆ and C₄ acting via C₄/C₂=C₂	64		D16:2C4	128,147
D₁₆.C₄	1^st non-split extension by D₁₆ of C₄ acting via C₄/C₂=C₂	64	2	D16.C4	128,149
C₁₆.₁₈D₄	4^th non-split extension by C₁₆ of D₄ acting via D₄/C₂²=C₂	64	4-	C16.18D4	128,152
C₃₂.C₄	1^st non-split extension by C₃₂ of C₄ acting via C₄/C₂=C₂	64	2	C32.C4	128,157
M₇(2)	Modular maximal-cyclic group; = C₆₄ ⋊₃ C₂	64	2	M7(2)	128,160
D₆₄	Dihedral group	64	2+	D64	128,161
SD₁₂₈	Semidihedral group; = C₆₄ ⋊₂ C₂ = QD₁₂₈	64	2	SD128	128,162
C₂⁴.₁₇Q₈	1^st non-split extension by C₂⁴ of Q₈ acting via Q₈/C₄=C₂	64		C2^4.17Q8	128,165
C₂³⋊₂C₄²	1^st semidirect product of C₂³ and C₄² acting via C₄²/C₂²=C₂²	64		C2^3:2C4^2	128,169
C₂⁴.₅₀D₄	5^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	64		C2^4.50D4	128,170
C₂⁴.₅Q₈	4^th non-split extension by C₂⁴ of Q₈ acting via Q₈/C₂=C₂²	64		C2^4.5Q8	128,171
C₂⁴.₅₂D₄	7^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	64		C2^4.52D4	128,172
C₈×M₄(2)	Direct product of C₈ and M₄(2)	64		C8xM4(2)	128,181
C₈²⋊C₂	1^st semidirect product of C₈² and C₂ acting faithfully	64		C8^2:C2	128,182
C₈⋊₉M₄(2)	3^rd semidirect product of C₈ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	64		C8:9M4(2)	128,183
C₂³.₂₇C₄²	9^th non-split extension by C₂³ of C₄² acting via C₄²/C₂×C₄=C₂	64		C2^3.27C4^2	128,184
C₈²⋊₁₅C₂	15^th semidirect product of C₈² and C₂ acting faithfully	64		C8^2:15C2	128,185
C₈²⋊₂C₂	2^nd semidirect product of C₈² and C₂ acting faithfully	64		C8^2:2C2	128,186
C₈⋊₆M₄(2)	3^rd semidirect product of C₈ and M₄(2) acting via M₄(2)/C₈=C₂	64		C8:6M4(2)	128,187
C₂×C₂².M₄(2)	Direct product of C₂ and C₂².M₄(2)	64		C2xC2^2.M4(2)	128,189
C₄².₃₉₄D₄	27^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.394D4	128,193
C₄².₄₄D₄	26^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.44D4	128,199
C₄².₃₉₆D₄	29^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.396D4	128,202
C₂×D₄⋊C₈	Direct product of C₂ and D₄⋊C₈	64		C2xD4:C8	128,206
C₄².₄₅₅D₄	4^th central extension by C₄² of D₄	64		C4^2.455D4	128,208
C₄².₃₉₇D₄	30^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.397D4	128,209
C₄².₃₉₉D₄	32^nd non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.399D4	128,211
C₄².₄₅D₄	27^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.45D4	128,212
C₄².₄₆D₄	28^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.46D4	128,213
C₄².₃₇₃D₄	6^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.373D4	128,214
C₄².₄₇D₄	29^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.47D4	128,215
C₄².₄₀₀D₄	33^rd non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.400D4	128,216
C₄².₄₀₁D₄	34^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.401D4	128,217
Q₈⋊M₄(2)	1^st semidirect product of Q₈ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	64		Q8:M4(2)	128,219
C₄².₃₇₄D₄	7^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.374D4	128,220
D₄⋊₄M₄(2)	2^nd semidirect product of D₄ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	64		D4:4M4(2)	128,221
Q₈⋊₅M₄(2)	3^rd semidirect product of Q₈ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	64		Q8:5M4(2)	128,223
C₄².₃₁₅D₄	11^st non-split extension by C₄² of D₄ acting via D₄/C₄=C₂	64		C4^2.315D4	128,224
C₄².₃₁₆D₄	12^nd non-split extension by C₄² of D₄ acting via D₄/C₄=C₂	64		C4^2.316D4	128,225
C₄².₃₀₅D₄	1^st non-split extension by C₄² of D₄ acting via D₄/C₄=C₂	64		C4^2.305D4	128,226
C₄².₅₂D₄	34^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.52D4	128,227
C₄².₅₃D₄	35^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.53D4	128,228
C₄².₅₄D₄	36^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.54D4	128,229
C₂×C₄².C₂²	Direct product of C₂ and C₄².C₂²	64		C2xC4^2.C2^2	128,254
C₄².₆₆D₄	48^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.66D4	128,256
C₄².₄₀₅D₄	38^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.405D4	128,257
C₄².₄₀₆D₄	39^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.406D4	128,258
C₄².₄₀₈D₄	41^st non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.408D4	128,260
C₄².₃₇₆D₄	9^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.376D4	128,261
C₄².₆₇D₄	49^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.67D4	128,262
C₄².₆₈D₄	50^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.68D4	128,263
C₄².₆₉D₄	51^st non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.69D4	128,264
C₄².₇₁D₄	53^rd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.71D4	128,266
C₄².₇₂D₄	54^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.72D4	128,267
C₄².₇₃D₄	55^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.73D4	128,268
C₄².₇₄D₄	56^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.74D4	128,269
C₂×C₄.D₈	Direct product of C₂ and C₄.D₈	64		C2xC4.D8	128,270
C₄².₄₀₉D₄	42^nd non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.409D4	128,272
C₄².₄₁₀D₄	43^rd non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.410D4	128,274
C₄².₄₁₁D₄	44^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.411D4	128,275
C₄².₄₁₂D₄	45^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.412D4	128,276
C₄².₄₁₄D₄	47^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.414D4	128,278
C₄².₇₈D₄	60^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.78D4	128,279
C₄².₄₁₅D₄	48^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.415D4	128,280
C₄².₄₁₆D₄	49^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.416D4	128,281
C₄².₇₉D₄	61^st non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.79D4	128,282
C₄².₈₀D₄	62^nd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.80D4	128,283
C₄².₈₁D₄	63^rd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.81D4	128,284
C₄².₄₁₇D₄	50^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.417D4	128,285
C₄².₄₁₈D₄	51^st non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	64		C4^2.418D4	128,286
C₄².₈₃D₄	65^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.83D4	128,288
C₄².₈₄D₄	66^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.84D4	128,289
C₄².₈₅D₄	67^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.85D4	128,290
C₄².₈₆D₄	68^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.86D4	128,291
C₄².₈₇D₄	69^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.87D4	128,292
C₄².₈₈D₄	70^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.88D4	128,293
C₄².₄₂Q₈	2^nd non-split extension by C₄² of Q₈ acting via Q₈/C₄=C₂	64		C4^2.42Q8	128,296
M₄(2)⋊₁C₈	1^st semidirect product of M₄(2) and C₈ acting via C₈/C₄=C₂	64		M4(2):1C8	128,297
C₈⋊₈M₄(2)	2^nd semidirect product of C₈ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	64		C8:8M4(2)	128,298
C₈⋊₇M₄(2)	1^st semidirect product of C₈ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	64		C8:7M4(2)	128,299
C₄².₄₃Q₈	3^rd non-split extension by C₄² of Q₈ acting via Q₈/C₄=C₂	64		C4^2.43Q8	128,300
C₈⋊₁M₄(2)	1^st semidirect product of C₈ and M₄(2) acting via M₄(2)/C₄=C₂²	64		C8:1M4(2)	128,301
C₄².₉₀D₄	72^nd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.90D4	128,302
C₄².₉₁D₄	73^rd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.91D4	128,303
C₄².Q₈	19^th non-split extension by C₄² of Q₈ acting via Q₈/C₂=C₂²	64		C4^2.Q8	128,304
C₄².₉₂D₄	74^th non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	64		C4^2.92D4	128,305
C₄².₂₁Q₈	21^st non-split extension by C₄² of Q₈ acting via Q₈/C₂=C₂²	64		C4^2.21Q8	128,306
C₈×D₈	Direct product of C₈ and D₈	64		C8xD8	128,307
C₈×SD₁₆	Direct product of C₈ and SD₁₆	64		C8xSD16	128,308
SD₁₆⋊C₈	The semidirect product of SD₁₆ and C₈ acting via C₈/C₄=C₂	64		SD16:C8	128,310
D₈⋊₅C₈	5^th semidirect product of D₈ and C₈ acting via C₈/C₄=C₂	64		D8:5C8	128,312
C₈⋊₉D₈	3^rd semidirect product of C₈ and D₈ acting via D₈/D₄=C₂	64		C8:9D8	128,313
C₈⋊₁₂SD₁₆	3^rd semidirect product of C₈ and SD₁₆ acting via SD₁₆/D₄=C₂	64		C8:12SD16	128,314
C₈⋊₁₅SD₁₆	3^rd semidirect product of C₈ and SD₁₆ acting via SD₁₆/Q₈=C₂	64		C8:1