Subgroups — #22582513

Order 8991.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688521	C₃	1	1	yes	maximal, characteristic, complemented
2	#15688519	C₃	1	2	yes	maximal, complemented
3	C₃₇×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×C₃₇	—	3	1	no	—
5	C₃×C₉×C₃₇	C₃²	1	1	yes	characteristic
6	C₃²⋊(C₃₇⋊C₃)	—	3	2	no	—
7	#11758608	—	3	1	no	—
8	C₃²×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
9	C₃×C₃₇⋊C₃	—	9	2	no	—
10	C₉×C₃₇	—	3	1	no	—
11	C₉×C₃₇	—	9	1	no	—
12	#66524	—	9	1	no	—
13	#6881	—	37	1	no	maximal, Sylow
14	C₃×C₃₇	—	3	1	no	—
15	C₃×C₃₇	#732	1	1	yes	characteristic
16	C₃₇⋊C₃	—	27	2	no	—
17	#733	—	37	1	no	—
18	#732	—	37	2	no	—
19	C₉⋊C₉	C₃₇⋊C₃	1	1	yes	characteristic, complemented
20	C₃₇	#6881	1	1	yes	characteristic, complemented, Sylow
21	3₋¹⁺²	—	111	1	no	—
22	H(3,𝔽₃)	—	111	2	no	—
23	C₃×C₉	—	3	1	no	—
24	C₃×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
25	C₃²	—	333	2	no	—
26	C₃²	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
27	C₉	—	3	1	no	—
28	C₉	—	9	1	no	—
29	C₉	—	333	1	no	—
30	C₃	—	3	1	no	—
31	C₃	—	999	2	no	—
32	C₃	#15688519	1	1	yes	characteristic

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