Subgroups — #10619570

Order 648.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₉	C₃	1	1	yes	maximal, characteristic
2	Q₈⋊C₂₇	C₃	1	3	yes	maximal, complemented
3	C₂×C₂₇⋊C₃	—	4	1	no	maximal
4	C₃×C₄×C₉	—	3	1	no	—
5	C₂₇⋊C₃	—	4	1	no	Sylow
6	C₃²×Q₈	C₉	1	1	yes	characteristic
7	Q₈×C₉	C₉	1	2	yes	—
8	Q₈×C₉	C₃²	1	1	yes	characteristic
9	C₂×C₃×C₉	A₄	1	1	yes	characteristic
10	C₂×C₂₇	—	4	3	no	—
11	C₃²×C₄	—	3	1	no	—
12	C₄×C₉	—	3	2	no	—
13	C₄×C₉	—	3	1	no	—
14	C₃×C₉	SL(2,𝔽₃)	1	1	yes	characteristic
15	C₂₇	—	4	3	no	—
16	C₃×Q₈	—	3	1	no	—
17	C₃×Q₈	C₃×C₉	1	1	yes	characteristic
18	C₂×C₃²	C₂²⋊C₉	1	1	yes	characteristic
19	C₂×C₉	C₂²⋊C₉	1	2	yes	—
20	C₂×C₉	C₃×A₄	1	1	yes	characteristic
21	C₃×C₄	—	3	3	no	—
22	C₃×C₄	—	3	1	no	—
23	C₃²	Q₈⋊C₉	1	1	yes	characteristic
24	C₉	Q₈⋊C₉	1	2	yes	—
25	C₉	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
26	Q₈	C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	3	1	no	—
28	C₂×C₃	C₃×C₂²⋊C₉	1	1	yes	characteristic
29	C₄	—	3	1	no	—
30	C₃	—	3	1	no	—
31	C₃	C₃×Q₈⋊C₉	1	1	yes	characteristic
32	C₂	#66353	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. Q₈⋊C₂₇	C₃	semidirect
26. Q₈	C₂₇⋊C₃	semidirect

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