Subgroups — #41005055

Order 26973.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582500	C₃	1	3	yes	maximal
2	C₃₇×#6864	C₃	1	1	yes	maximal, characteristic
3	#15688500	—	3	3	no	—
4	C₃×C₂₇×C₃₇	C₉	1	1	yes	characteristic
5	C₃×C₂₇×C₃₇	C₉	1	1	yes	characteristic
6	C₃×C₂₇×C₃₇	C₃²	1	1	yes	characteristic
7	C₉²×C₃₇	C₉	1	1	yes	characteristic
8	C₃×C₉×C₃₇	—	3	1	no	—
9	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
10	C₂₇×C₃₇	—	3	1	no	—
11	C₂₇×C₃₇	C₂₇	1	3	yes	—
12	C₂₇×C₃₇	3₋¹⁺²	1	3	yes	—
13	#10624532	—	37	1	no	maximal, Sylow
14	C₃²×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
15	C₉×C₃₇	—	9	1	no	—
16	C₉×C₃₇	C₉⋊C₉	1	1	yes	characteristic
17	C₉×C₃₇	C₃×C₂₇	1	1	yes	characteristic
18	C₉×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
19	C₈₁⋊C₃	—	37	3	no	—
20	#6864	C₃₇⋊C₃	1	1	yes	characteristic
21	C₃×C₃₇	—	3	1	no	—
22	C₃×C₃₇	C₉⋊C₂₇	1	1	yes	characteristic
23	C₃×C₂₇	#66524	1	1	yes	characteristic
24	C₃×C₂₇	#66524	1	1	yes	characteristic
25	C₃×C₂₇	C₃×C₃₇⋊C₃	1	1	yes	characteristic
26	C₉²	#66524	1	1	yes	characteristic
27	C₈₁	—	111	3	no	—
28	C₃₇	#10624532	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₉	—	3	1	no	—
30	C₃×C₉	C₃×#66524	1	1	yes	characteristic
31	C₂₇	—	3	1	no	—
32	C₂₇	#11758601	1	3	yes	—
33	C₂₇	#11758606	1	3	yes	—
34	C₃²	#15688511	1	1	yes	characteristic
35	C₉	—	9	1	no	—
36	C₉	#15688506	1	1	yes	characteristic
37	C₉	C₃×#11758601	1	1	yes	characteristic
38	C₉	#15688511	1	1	yes	characteristic
39	C₃	—	3	1	no	—
40	C₃	#22582490	1	1	yes	characteristic

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

N	H ≅ G/N	type
28. C₃₇	#10624532	semidirect

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