Subgroups — #22582688

Order 8991.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11758603	C₃	1	3	yes	maximal
2	C₉×#66524	C₃	1	1	yes	maximal, characteristic
3	C₃×C₉×C₃₇	C₉	1	1	yes	characteristic
4	C₃×#66524	C₉	1	1	yes	characteristic
5	C₃×#66524	C₉	1	1	yes	characteristic
6	C₃×#66524	C₃²	1	1	yes	characteristic
7	#11758603	C₉	1	9	yes	complemented
8	C₃²×C₃₇	C₃×C₉	1	1	yes	characteristic
9	C₉×C₃₇	—	3	1	no	—
10	#66524	—	3	1	no	—
11	#66524	—	3	1	no	—
12	#66524	C₃×C₉	1	3	yes	—
13	#6864	—	37	1	no	maximal, Sylow
14	C₃×C₃₇	C₉²	1	1	yes	characteristic
15	C₃×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
16	C₃×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
17	C₃×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
18	C₃×C₂₇	—	37	3	no	—
19	C₉²	—	37	1	no	—
20	C₃₇	#6864	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₉	—	37	1	no	—
22	C₃×C₉	—	37	1	no	—
23	C₃×C₉	—	37	1	no	—
24	C₃×C₉	#66526	1	1	yes	characteristic
25	C₂₇	—	37	9	no	—
26	C₃²	C₃×#66526	1	1	yes	characteristic
27	C₉	—	3	1	no	—
28	C₉	—	37	3	no	—
29	C₉	—	111	1	no	—
30	C₉	—	111	1	no	—
31	C₃	C₉×#66526	1	1	yes	characteristic
32	C₃	#15688541	1	1	yes	characteristic
33	C₃	#15688542	1	1	yes	characteristic
34	C₃	#15688543	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. #11758603	C₉	semidirect
20. C₃₇	#6864	semidirect