Subgroups — #63578

Order 288.

71 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₃×#208	C₂	1	2	yes	maximal
3	#822	—	3	2	no	maximal
4	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
5	C₃⋊(C₃⋊C₈)	C₄	1	2	yes	—
6	C₃×C₃⋊C₈	—	2	2	no	—
7	C₃×M₁₆	—	3	2	no	—
8	#208	D₃	1	2	yes	—
9	C₂×C₃⋊C₈	—	3	2	no	—
10	C₂×C₃⋊C₈	—	6	1	no	—
11	C₂²×C₃²	Q₈	1	1	yes	characteristic
12	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
13	C₃²×C₄	D₄	1	1	yes	characteristic
14	#108	—	9	1	no	Sylow
15	C₂×C₃×C₄	—	2	1	no	—
16	C₂×C₃×C₄	C₂×D₃	1	2	yes	—
17	C₃×C₈	—	6	2	no	—
18	C₃⋊C₈	—	2	2	no	—
19	C₃⋊C₈	—	3	4	no	—
20	C₃⋊C₈	—	6	2	no	—
21	C₂×C₃²	—	2	1	no	—
22	C₂×C₃²	C₄⋊C₄	1	1	yes	characteristic
23	M₁₆	—	3	2	no	—
24	C₂×C₈	—	9	1	no	—
25	C₂²×C₃	—	2	1	no	—
26	C₂²×C₃	Dic₆	1	2	yes	—
27	C₃×C₄	—	2	1	no	—
28	C₃×C₄	—	2	1	no	—
29	C₃×C₄	C₄×D₃	1	2	yes	—
30	C₃×C₄	#67	1	2	yes	—
31	C₃²	#108	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₄	D₃²	1	1	yes	characteristic
33	C₈	—	6	2	no	—
34	C₈	—	9	2	no	—
35	C₂×C₃	—	2	2	no	—
36	C₂×C₃	—	2	2	no	—
37	C₂×C₃	—	2	1	no	—
38	C₂×C₃	Dic₃⋊C₄	1	2	yes	—
39	C₂²	#627	1	1	yes	characteristic
40	C₄	#624	1	1	yes	characteristic
41	C₄	#625	1	1	yes	characteristic
42	C₃	—	2	1	no	—
43	C₃	#822	1	2	yes	complemented
44	C₂	—	2	1	no	—
45	C₂	#3724	1	1	yes	characteristic

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

N	H ≅ G/N	type
31. C₃²	#108	semidirect
43. C₃	#822	semidirect

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