Subgroups — #63779

Order 288.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#622	C₂	1	2	yes	maximal
2	C₄×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
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	#622	—	2	2	no	—
7	C₄×Dic₃	—	6	2	no	—
8	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
9	C₃²×C₄	—	2	1	no	—
10	C₃⋊Dic₃	C₈	1	2	yes	complemented
11	C₃⋊Dic₃	D₄	1	1	yes	characteristic
12	C₃⋊Dic₃	Q₈	1	1	yes	characteristic
13	C₄⋊C₈	—	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	C₂×C₃²	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₃²	C₂×C₈	1	1	yes	characteristic
19	C₂×C₃²	M₁₆	1	1	yes	characteristic
20	C₂×C₈	—	9	2	no	—
21	C₄²	—	9	1	no	—
22	C₂²×C₃	—	2	2	no	—
23	C₃×C₄	—	2	4	no	—
24	Dic₃	—	6	4	no	—
25	Dic₃	—	6	2	no	—
26	Dic₃	—	6	2	no	—
27	C₃²	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
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	2	no	—
33	C₂×C₃	—	2	2	no	—
34	C₂×C₃	—	2	2	no	—
35	C₂²	C₂×#157	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	—	9	2	no	—
38	C₄	—	9	1	no	—
39	C₄	—	9	1	no	—
40	C₃	—	2	2	no	—
41	C₂	#3787	1	1	yes	characteristic
42	C₂	C₄⋊#157	1	1	yes	characteristic
43	C₂	#3792	1	1	yes	characteristic

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

N	H ≅ G/N	type
10. C₃⋊Dic₃	C₈	semidirect
27. C₃²	C₄⋊C₈	semidirect

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