Subgroups — #41004777

Order 26973.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊#11758601	C₃	1	3	yes	maximal
2	C₃₇×#6887	C₃	1	1	yes	maximal, characteristic
3	C₃×#11758601	—	3	3	no	—
4	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
5	C₃₇×C₉⋊C₉	—	3	2	no	—
6	C₃₇×C₃²⋊C₉	C₉	1	3	yes	—
7	C₉²×C₃₇	—	3	1	no	—
8	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
9	C₃×C₉×C₃₇	—	3	3	no	—
10	C₃×C₉×C₃₇	—	3	3	no	—
11	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃×C₉×C₃₇	3₋¹⁺²	1	2	yes	—
13	#11758601	—	9	3	no	—
14	#10624457	—	37	1	no	maximal, Sylow
15	C₃²×C₃₇	—	3	1	no	—
16	C₃²×C₃₇	—	3	3	no	—
17	C₃²×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
18	C₉×C₃₇	—	3	2	no	—
19	C₉×C₃₇	—	9	3	no	—
20	C₉×C₃₇	#731	1	3	yes	—
21	#6887	C₃₇⋊C₃	1	1	yes	characteristic
22	C₃²⋊C₂₇	—	37	3	no	—
23	C₃×C₃₇	—	9	1	no	—
24	C₃×C₃₇	#6867	1	1	yes	characteristic
25	C₃×C₃₇	#6872	1	3	yes	—
26	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
27	C₃×C₂₇	—	111	3	no	—
28	C₉⋊C₉	—	3	2	no	—
29	C₃²⋊C₉	#66524	1	3	yes	—
30	C₉²	—	3	1	no	—
31	C₃₇	#10624457	1	1	yes	characteristic, complemented, Sylow
32	C₃³	C₃×#66524	1	1	yes	characteristic
33	C₃×C₉	—	3	3	no	—
34	C₃×C₉	—	3	3	no	—
35	C₃×C₉	#11758608	1	2	yes	—
36	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
37	C₂₇	—	333	3	no	—
38	C₃²	—	3	1	no	—
39	C₃²	—	3	3	no	—
40	C₃²	C₃²⋊#66524	1	1	yes	characteristic
41	C₉	—	3	2	no	—
42	C₉	—	9	3	no	—
43	C₉	#15688516	1	3	yes	—
44	C₃	—	9	1	no	—
45	C₃	#22582470	1	1	yes	characteristic
46	C₃	#22582483	1	3	yes	—

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

N	H ≅ G/N	type
31. C₃₇	#10624457	semidirect

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