Subgroups — #63550

Order 288.

53 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Dic₁₂	C₂	1	2	yes	maximal
2	C₃⋊(C₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	#829	—	3	2	no	maximal
4	C₃×Dic₆	—	2	2	no	—
5	C₃²×C₈	C₂²	1	1	yes	characteristic
6	C₃×Q₁₆	—	3	2	no	—
7	Dic₁₂	D₃	1	2	yes	—
8	C₃⋊C₁₆	—	3	2	no	—
9	C₃⋊C₁₆	—	6	1	no	—
10	C₃²×C₄	D₄	1	1	yes	characteristic
11	C₃×Dic₃	—	4	2	no	—
12	Q₃₂	—	9	1	no	Sylow
13	C₃×Q₈	—	6	2	no	—
14	Dic₆	—	2	2	no	—
15	C₃×C₈	—	2	1	no	—
16	C₃×C₈	C₂×D₃	1	2	yes	—
17	C₂×C₃²	D₈	1	1	yes	characteristic
18	Q₁₆	—	3	2	no	—
19	C₁₆	—	9	1	no	—
20	C₃×C₄	—	2	1	no	—
21	C₃×C₄	—	12	2	no	—
22	C₃×C₄	#67	1	2	yes	—
23	Dic₃	—	4	2	no	—
24	C₃²	Q₃₂	1	1	yes	characteristic, complemented, Sylow
25	Q₈	—	6	2	no	—
26	C₈	D₃²	1	1	yes	characteristic
27	C₂×C₃	—	2	1	no	—
28	C₂×C₃	#213	1	2	yes	—
29	C₄	—	12	2	no	—
30	C₄	#625	1	1	yes	characteristic
31	C₃	—	2	1	no	—
32	C₃	#829	1	2	yes	complemented
33	C₂	#3713	1	1	yes	characteristic

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

N	H ≅ G/N	type
24. C₃²	Q₃₂	semidirect
32. C₃	#829	semidirect

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