Subgroups — #22582652

Order 8991.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11758608	C₃	1	3	yes	maximal
2	#15688521	C₃	1	9	yes	maximal, complemented
3	C₃×3₋¹⁺²×C₃₇	C₃	1	1	yes	maximal, characteristic
4	C₃³×C₃₇	C₃²	1	1	yes	characteristic
5	3₋¹⁺²×C₃₇	—	3	3	no	—
6	C₃×C₉×C₃₇	C₃²	1	3	yes	—
7	#11758608	—	3	6	no	—
8	#11758608	C₃²	1	9	yes	—
9	C₃×#66524	—	3	3	no	—
10	C₃²×C₃₇	—	9	1	no	—
11	C₃²×C₃₇	H(3,𝔽₃)	1	3	yes	—
12	C₃²×C₃₇	C₃³	1	1	yes	characteristic
13	C₉×C₃₇	—	3	3	no	—
14	#66524	—	3	9	no	—
15	#6912	—	37	1	no	maximal, Sylow
16	C₃×C₃₇	—	3	3	no	—
17	C₃×C₃₇	—	3	1	no	—
18	C₃×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
19	C₃×3₋¹⁺²	—	37	3	no	—
20	C₃×3₋¹⁺²	C₃₇⋊C₃	1	1	yes	characteristic
21	#733	—	37	9	no	—
22	C₃₇	#6912	1	1	yes	characteristic, complemented, Sylow
23	C₃³	C₃×C₃₇⋊C₃	1	1	yes	characteristic
24	3₋¹⁺²	—	3	3	no	—
25	3₋¹⁺²	—	37	9	no	—
26	3₋¹⁺²	—	111	6	no	—
27	C₃×C₉	—	111	3	no	—
28	C₃×C₉	C₃×C₃₇⋊C₃	1	3	yes	—
29	C₃²	—	9	1	no	—
30	C₃²	C₃²⋊(C₃₇⋊C₃)	1	3	yes	—
31	C₃²	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
32	C₉	—	3	3	no	—
33	C₉	—	111	9	no	—
34	C₃	—	3	3	no	—
35	C₃	—	3	1	no	—
36	C₃	C₃×C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #15688521	C₃	semidirect
22. C₃₇	#6912	semidirect