Subgroups — #63780

Order 288.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#634	C₂	1	1	yes	maximal, characteristic
2	#3792	C₂	1	2	yes	maximal
3	C₂×C₃²×C₄	C₄	1	1	yes	characteristic
4	C₂×C₃⋊Dic₃	C₄	1	1	yes	characteristic
5	C₂×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
6	#634	—	2	2	no	—
7	#622	—	2	2	no	—
8	C₂×Dic₆	—	6	2	no	—
9	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
10	C₃²×C₄	—	2	1	no	—
11	C₃⋊Dic₃	—	2	1	no	—
12	C₃⋊Dic₃	D₄	1	2	yes	—
13	#101	—	9	1	no	maximal, Sylow
14	C₂×C₃×C₄	—	2	2	no	—
15	C₂×Dic₃	—	6	2	no	—
16	C₂×Dic₃	—	6	2	no	—
17	Dic₆	—	6	8	no	—
18	C₂×C₃²	—	2	1	no	—
19	C₂×C₃²	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×Q₈	—	9	1	no	—
21	M₁₆	—	9	2	no	—
22	C₂²×C₃	—	2	2	no	—
23	C₃×C₄	—	2	4	no	—
24	Dic₃	—	6	4	no	—
25	Dic₃	—	6	4	no	—
26	C₃²	#101	1	1	yes	characteristic, complemented, Sylow
27	Q₈	—	18	2	no	—
28	C₂×C₄	—	9	1	no	—
29	C₂×C₄	—	9	1	no	—
30	C₂×C₄	#157	1	1	yes	characteristic
31	C₈	—	18	2	no	—
32	C₂×C₃	—	2	4	no	—
33	C₂×C₃	—	2	2	no	—
34	C₂²	C₂×#157	1	1	yes	characteristic
35	C₄	—	2	1	no	—
36	C₄	—	9	2	no	—
37	C₄	—	18	1	no	—
38	C₃	—	2	2	no	—
39	C₂	—	2	1	no	—
40	C₂	C₂²⋊#157	1	1	yes	characteristic

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

N	H ≅ G/N	type
26. C₃²	#101	semidirect

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