Subgroups — #63561

Order 288.

95 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	C₃×#208	C₂	1	2	yes	maximal
3	#824	—	3	2	no	maximal
4	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
5	C₂×C₃⋊Dic₃	C₄	1	2	yes	—
6	#634	—	2	2	no	—
7	C₃×C₃⋊C₈	—	2	2	no	—
8	C₂×Dic₆	—	3	2	no	—
9	C₂×Dic₆	—	6	1	no	—
10	C₃×M₁₆	—	3	2	no	—
11	#208	D₃	1	2	yes	—
12	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
13	C₃²×C₄	D₄	1	2	yes	—
14	C₃⋊Dic₃	—	2	2	no	—
15	#101	—	9	1	no	Sylow
16	C₂×C₃×C₄	—	2	1	no	—
17	C₂×C₃×C₄	C₂×D₃	1	2	yes	—
18	C₂×Dic₃	—	3	4	no	—
19	C₂×Dic₃	—	6	2	no	—
20	Dic₆	—	6	4	no	—
21	Dic₆	—	6	2	no	—
22	Dic₆	—	6	2	no	—
23	C₃×C₈	—	6	2	no	—
24	C₃⋊C₈	—	2	2	no	—
25	C₂×C₃²	—	2	1	no	—
26	C₂×C₃²	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Q₈	—	9	1	no	—
28	M₁₆	—	3	2	no	—
29	C₂²×C₃	—	2	1	no	—
30	C₂²×C₃	C₄×D₃	1	2	yes	—
31	C₃×C₄	—	2	2	no	—
32	C₃×C₄	D₁₂	1	2	yes	—
33	C₃×C₄	#67	1	2	yes	—
34	Dic₃	—	6	4	no	—
35	Dic₃	—	6	4	no	—
36	C₃²	#101	1	1	yes	characteristic, complemented, Sylow
37	Q₈	—	18	2	no	—
38	C₂×C₄	—	9	2	no	—
39	C₂×C₄	D₃²	1	1	yes	characteristic
40	C₈	—	6	2	no	—
41	C₂×C₃	—	2	2	no	—
42	C₂×C₃	—	2	2	no	—
43	C₂×C₃	—	2	1	no	—
44	C₂×C₃	(C₂×D₃)⋊C₄	1	2	yes	—
45	C₂²	#624	1	1	yes	characteristic
46	C₄	—	18	2	no	—
47	C₄	#626	1	2	yes	—
48	C₃	—	2	1	no	—
49	C₃	#824	1	2	yes	complemented
50	C₂	—	2	1	no	—
51	C₂	#3722	1	1	yes	characteristic

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

N	H ≅ G/N	type
36. C₃²	#101	semidirect
49. C₃	#824	semidirect

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