Subgroups — #41008431

Order 26973.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582682	C₃	1	3	yes	maximal, complemented
2	C₈₁×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₂₇×C₃₇⋊C₃	C₉	1	1	yes	characteristic
4	#15688500	C₉	1	1	yes	characteristic
5	#15688500	C₃²	1	1	yes	characteristic
6	C₃₇×C₈₁	C₉	1	1	yes	characteristic
7	C₉×C₃₇⋊C₃	C₂₇	1	1	yes	characteristic
8	C₂₇×C₃₇	C₃×C₉	1	1	yes	characteristic
9	#11758601	C₂₇	1	2	yes	—
10	C₂₄₃⋊C₃	—	37	1	no	maximal, Sylow
11	C₃×C₃₇⋊C₃	C₈₁	1	1	yes	characteristic
12	C₉×C₃₇	C₃×C₂₇	1	1	yes	characteristic
13	#66524	C₈₁	1	2	yes	—
14	C₃×C₈₁	—	37	1	no	—
15	C₂₄₃	—	37	3	no	—
16	C₃×C₃₇	C₃×C₈₁	1	1	yes	characteristic
17	C₃₇⋊C₃	—	3	1	no	—
18	C₃×C₂₇	—	37	1	no	—
19	C₈₁	—	37	1	no	—
20	C₈₁	—	37	1	no	—
21	C₈₁	#66526	1	1	yes	characteristic
22	C₃₇	C₂₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₃×C₉	—	37	1	no	—
24	C₂₇	—	37	2	no	—
25	C₂₇	C₃×#66526	1	1	yes	characteristic
26	C₃²	—	37	1	no	—
27	C₉	—	37	2	no	—
28	C₉	(C₃₇⋊C₃)⋊C₂₇	1	1	yes	characteristic
29	C₃	—	111	1	no	—
30	C₃	(C₃₇⋊C₃)⋊C₈₁	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #22582682	C₃	semidirect
22. C₃₇	C₂₄₃⋊C₃	semidirect

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