Subgroups — #41008430

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	C₃×#15688500	C₃	1	1	yes	maximal, characteristic
3	#15688500	C₉	1	2	yes	—
4	#15688500	C₃²	1	1	yes	characteristic
5	C₃×C₂₇×C₃₇	C₉	1	1	yes	characteristic
6	C₃×C₉×C₃₇	C₂₇	1	1	yes	characteristic
7	C₂₇×C₃₇	C₂₇	1	2	yes	—
8	C₂₇×C₃₇	C₃×C₉	1	1	yes	characteristic
9	C₂₄₃⋊C₃	—	37	1	no	maximal, Sylow
10	C₃²×C₃₇	C₈₁	1	1	yes	characteristic
11	C₉×C₃₇	C₈₁	1	2	yes	—
12	C₉×C₃₇	C₃×C₂₇	1	1	yes	characteristic
13	C₃×C₈₁	—	37	1	no	—
14	C₂₄₃	—	37	3	no	—
15	C₃×C₃₇	—	3	1	no	—
16	C₃×C₃₇	C₃×C₈₁	1	1	yes	characteristic
17	C₃×C₂₇	#66526	1	1	yes	characteristic
18	C₈₁	—	37	2	no	—
19	C₈₁	—	37	1	no	—
20	C₃₇	C₂₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₉	#11758603	1	1	yes	characteristic
22	C₂₇	#11758603	1	2	yes	—
23	C₂₇	C₃×#66526	1	1	yes	characteristic
24	C₃²	#15688534	1	1	yes	characteristic
25	C₉	#15688534	1	2	yes	—
26	C₉	C₃×#11758603	1	1	yes	characteristic
27	C₃	—	3	1	no	—
28	C₃	C₃×#15688534	1	1	yes	characteristic

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

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

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