Subgroups — #22582587

Order 8991.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688504	C₃	1	8	yes	maximal, complemented
2	#15688502	C₃	1	4	yes	maximal
3	C₉²×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₃₇	C₃²	1	4	yes	—
6	C₃×#66524	C₃²	1	8	yes	—
7	C₃²×C₃₇	C₃³	1	1	yes	characteristic
8	C₃×C₃₇⋊C₃	—	3	4	no	—
9	C₉×C₃₇	—	3	4	no	—
10	#66524	—	3	8	no	—
11	#6897	—	37	1	no	maximal, Sylow
12	C₃×C₃₇	#737	1	4	yes	—
13	C₃₇⋊C₃	—	9	1	no	—
14	C₉⋊C₉	—	37	8	no	—
15	C₃²⋊C₉	—	37	4	no	—
16	C₉²	C₃₇⋊C₃	1	1	yes	characteristic, complemented
17	C₃₇	#6897	1	1	yes	characteristic, complemented, Sylow
18	C₃³	—	37	1	no	—
19	C₃×C₉	—	37	8	no	—
20	C₃×C₉	C₃×C₃₇⋊C₃	1	4	yes	—
21	C₃²	—	111	4	no	—
22	C₃²	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
23	C₉	—	3	4	no	—
24	C₉	—	111	8	no	—
25	C₃	—	333	1	no	—
26	C₃	#15688531	1	4	yes	—

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