Subgroups — #41008357

Order 26973.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582715	C₃	1	3	yes	maximal
2	#22582462	C₃	1	1	yes	maximal, characteristic
3	#15688534	C₉	1	9	yes	complemented
4	C₃×#11758601	C₉	1	1	yes	characteristic
5	C₃×#11758601	C₃²	1	1	yes	characteristic
6	C₉×#66524	C₉	1	1	yes	characteristic
7	C₃×C₂₇×C₃₇	C₉	1	1	yes	characteristic
8	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
9	C₃×#66524	—	3	1	no	—
10	C₂₇×C₃₇	—	3	1	no	—
11	#11758601	—	3	1	no	—
12	#11758601	C₃×C₉	1	3	yes	—
13	#10624500	—	37	1	no	maximal, Sylow
14	C₃²×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
15	C₉×C₃₇	C₉²	1	1	yes	characteristic
16	C₉×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
17	C₉×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
18	#66524	—	9	1	no	—
19	C₈₁⋊C₃	—	37	3	no	—
20	#6864	—	37	1	no	—
21	C₃×C₃₇	—	3	1	no	—
22	C₃×C₃₇	#6864	1	1	yes	characteristic
23	C₃×C₂₇	—	37	1	no	—
24	C₃×C₂₇	—	37	1	no	—
25	C₃×C₂₇	#66526	1	1	yes	characteristic
26	C₉²	—	37	1	no	—
27	C₈₁	—	37	9	no	—
28	C₃₇	#10624500	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₉	—	111	1	no	—
30	C₃×C₉	C₃×#66526	1	1	yes	characteristic
31	C₂₇	—	3	1	no	—
32	C₂₇	—	37	3	no	—
33	C₂₇	—	111	1	no	—
34	C₃²	#15688543	1	1	yes	characteristic
35	C₉	—	333	1	no	—
36	C₉	C₉×#66526	1	1	yes	characteristic
37	C₉	#15688541	1	1	yes	characteristic
38	C₉	#15688542	1	1	yes	characteristic
39	C₃	—	3	1	no	—
40	C₃	#22582688	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #15688534	C₉	semidirect
28. C₃₇	#10624500	semidirect

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