Subgroups — #22582715

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	C₃×#11758601	C₃	1	1	yes	maximal, characteristic
3	C₃×C₉×C₃₇	C₉	1	1	yes	characteristic
4	#11758601	C₉	1	2	yes	—
5	#11758601	C₃²	1	1	yes	characteristic
6	C₃²×C₃₇	C₂₇	1	1	yes	characteristic
7	C₉×C₃₇	C₂₇	1	2	yes	—
8	C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
9	C₈₁⋊C₃	—	37	1	no	maximal, Sylow
10	C₃×C₃₇	—	3	1	no	—
11	C₃×C₃₇	C₃×C₂₇	1	1	yes	characteristic
12	C₃×C₂₇	—	37	1	no	—
13	C₈₁	—	37	3	no	—
14	C₃₇	C₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₉	#66526	1	1	yes	characteristic
16	C₂₇	—	37	2	no	—
17	C₂₇	—	37	1	no	—
18	C₃²	#11758603	1	1	yes	characteristic
19	C₉	#11758603	1	2	yes	—
20	C₉	C₃×#66526	1	1	yes	characteristic
21	C₃	—	3	1	no	—
22	C₃	C₃×#11758603	1	1	yes	characteristic

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

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