Subgroups — #63371

Order 288.

39 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₉⋊C₁₆	C₂	1	2	yes	maximal, complemented
3	#812	—	3	1	no	maximal
4	C₂×C₄×C₉	C₄	1	1	yes	characteristic
5	C₈×C₉	C₄	1	1	yes	characteristic
6	C₈×C₉	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₈	D₃	1	1	yes	characteristic
8	C₃⋊C₁₆	—	3	2	no	—
9	C₂²×C₉	C₈	1	1	yes	characteristic
10	C₄×C₉	C₈	1	1	yes	characteristic
11	C₄×C₉	C₂×C₄	1	1	yes	characteristic
12	M₃₂	—	9	1	no	Sylow
13	C₂×C₃×C₄	Dic₃	1	1	yes	characteristic
14	C₃×C₈	Dic₃	1	1	yes	characteristic
15	C₃×C₈	C₂×D₃	1	1	yes	characteristic
16	C₂×C₉	—	2	1	no	—
17	C₂×C₉	C₂×C₈	1	1	yes	characteristic
18	C₂×C₈	D₉	1	1	yes	characteristic
19	C₁₆	—	9	2	no	—
20	C₂²×C₃	C₃⋊C₈	1	1	yes	characteristic
21	C₃×C₄	C₃⋊C₈	1	1	yes	characteristic
22	C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
23	C₉	M₃₂	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₄	Dic₉	1	1	yes	characteristic
25	C₈	Dic₉	1	1	yes	characteristic
26	C₈	C₂×D₉	1	1	yes	characteristic
27	C₂×C₃	—	2	1	no	—
28	C₂×C₃	C₂×C₃⋊C₈	1	1	yes	characteristic
29	C₂²	C₉⋊C₈	1	1	yes	characteristic
30	C₄	C₉⋊C₈	1	1	yes	characteristic
31	C₄	C₂×Dic₉	1	1	yes	characteristic
32	C₃	#812	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×C₉⋊C₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₉⋊C₁₆	C₂	semidirect
23. C₉	M₃₂	semidirect

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