Subgroups — C₂×#10624562 #13090048

Order 1458.

2138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624562	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃²×H(3,𝔽₃)	C₃	1	13	yes	maximal, complemented
3	C₃²×H(3,𝔽₃)	C₂×C₃	1	13	yes	complemented
4	C₂×C₃⁴	C₃²	1	13	yes	—
5	C₂×C₃×H(3,𝔽₃)	—	3	156	no	—
6	C₃⁴	C₂×C₃²	1	13	yes	—
7	C₃×H(3,𝔽₃)	—	3	156	no	—
8	C₂×C₃³	—	3	156	no	—
9	C₂×C₃³	H(3,𝔽₃)	1	39	yes	complemented
10	C₂×C₃³	C₃³	1	1	yes	characteristic
11	C₂×H(3,𝔽₃)	—	3	351	no	—
12	C₃³	—	3	156	no	—
13	C₃³	C₂×H(3,𝔽₃)	1	39	yes	complemented
14	C₃³	C₂×C₃³	1	1	yes	characteristic
15	H(3,𝔽₃)	—	3	351	no	—
16	C₂×C₃²	—	3	156	no	—
17	C₂×C₃²	—	9	117	no	—
18	C₂×C₃²	C₃×H(3,𝔽₃)	1	13	yes	—
19	C₃²	—	3	156	no	—
20	C₃²	—	9	117	no	—
21	C₃²	C₂×C₃×H(3,𝔽₃)	1	13	yes	—
22	C₂×C₃	—	9	39	no	—
23	C₂×C₃	C₃²⋊H(3,𝔽₃)	1	13	yes	—
24	C₃	—	9	39	no	—
25	C₃	C₂×C₃²⋊H(3,𝔽₃)	1	13	yes	—
26	C₂	#10624562	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃³	C₃³
commutator, Frattini, cosocle	C₃³	C₂×C₃³
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₂×C₃³ ◁ G

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#10624562	2
C₂×C₃²×H(3,𝔽₃)	3