Subgroups — #63771

Order 288.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3788	C₂	1	2	yes	maximal
2	C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
3	C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
4	#622	—	2	2	no	—
5	C₃²×C₈	C₄	1	1	yes	characteristic
6	C₃⋊(C₃⋊C₈)	C₄	1	1	yes	characteristic
7	D₃×C₈	—	6	2	no	—
8	C₂×C₃⋊D₃	Q₈	1	1	yes	characteristic
9	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
10	C₃⋊Dic₃	D₄	1	1	yes	characteristic
11	#108	—	9	1	no	maximal, Sylow
12	C₄×D₃	—	6	2	no	—
13	C₃×C₈	—	2	2	no	—
14	C₃⋊C₈	—	6	2	no	—
15	C₂×C₃²	C₄⋊C₄	1	1	yes	characteristic
16	C₃⋊D₃	—	2	1	no	—
17	M₁₆	—	9	2	no	—
18	C₂×C₈	—	9	1	no	—
19	C₂×D₃	—	6	2	no	—
20	C₃×C₄	—	2	2	no	—
21	Dic₃	—	6	2	no	—
22	C₃²	#108	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₄	—	9	1	no	—
24	C₈	—	9	1	no	—
25	C₈	—	18	2	no	—
26	C₈	#157	1	1	yes	characteristic
27	C₂×C₃	—	2	2	no	—
28	D₃	—	6	4	no	—
29	C₂²	—	9	1	no	—
30	C₄	—	9	1	no	—
31	C₄	C₂×#157	1	1	yes	characteristic
32	C₃	—	2	2	no	—
33	C₂	—	18	1	no	—
34	C₂	C₄⋊#157	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₃²	#108	semidirect

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