Subgroups — #22582717

Order 8991.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688534	C₃	1	3	yes	maximal, complemented
2	C₂₇×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₉×C₃₇⋊C₃	C₉	1	1	yes	characteristic
4	C₂₇×C₃₇	C₉	1	1	yes	characteristic
5	#11758601	C₉	1	1	yes	characteristic
6	#11758601	C₃²	1	1	yes	characteristic
7	C₃×C₃₇⋊C₃	C₂₇	1	1	yes	characteristic
8	C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
9	#66524	C₂₇	1	2	yes	—
10	C₈₁⋊C₃	—	37	1	no	maximal, Sylow
11	C₃×C₃₇	C₃×C₂₇	1	1	yes	characteristic
12	C₃₇⋊C₃	—	3	1	no	—
13	C₃×C₂₇	—	37	1	no	—
14	C₈₁	—	37	3	no	—
15	C₃₇	C₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
16	C₃×C₉	—	37	1	no	—
17	C₂₇	—	37	1	no	—
18	C₂₇	—	37	1	no	—
19	C₂₇	#66526	1	1	yes	characteristic
20	C₃²	—	37	1	no	—
21	C₉	—	37	2	no	—
22	C₉	C₃×#66526	1	1	yes	characteristic
23	C₃	—	111	1	no	—
24	C₃	(C₃₇⋊C₃)⋊C₂₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #15688534	C₃	semidirect
15. C₃₇	C₈₁⋊C₃	semidirect