Subgroups — C₂₇×#66526 #22582684

Order 8991.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₃₇⋊C₃)⋊C₂₇	C₃	1	2	yes	maximal
2	C₉×#66526	C₃	1	1	yes	maximal, characteristic
3	C₂₇×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₃×#66526	C₉	1	3	yes	—
5	C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
6	#11758603	C₉	1	6	yes	complemented
7	C₂₇×C₃₇	C₉	1	1	yes	characteristic, complemented
8	#11758601	C₉	1	2	yes	complemented
9	C₃×C₃₇⋊C₃	C₃×C₉	1	1	yes	characteristic
10	#66526	C₂₇	1	9	yes	direct product factor
11	C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
12	#66524	C₃×C₉	1	2	yes	—
13	C₉×C₂₇	—	37	1	no	maximal, Sylow
14	C₃×C₃₇	C₉²	1	1	yes	characteristic
15	C₃₇⋊C₃	C₃×C₂₇	1	3	yes	—
16	C₃×C₂₇	—	37	2	no	—
17	C₃×C₂₇	—	37	1	no	—
18	C₉²	—	37	1	no	—
19	C₃₇	C₉×C₂₇	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₉	—	37	3	no	—
21	C₃×C₉	—	37	1	no	—
22	C₂₇	—	37	6	no	—
23	C₂₇	—	37	2	no	—
24	C₂₇	#66526	1	1	yes	characteristic, direct product factor
25	C₃²	—	37	1	no	—
26	C₉	—	37	9	no	—
27	C₉	—	37	2	no	—
28	C₉	C₃×#66526	1	1	yes	characteristic
29	C₃	—	37	3	no	—
30	C₃	C₉×#66526	1	1	yes	characteristic

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