Subgroups — #44525191

Order 30861.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779863	C₃	1	3	yes	maximal, complemented
2	C₂₇×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₂₇⋊C₃	C₉	1	1	yes	characteristic
4	#16812178	C₉	1	1	yes	characteristic
5	#16812178	C₃²	1	1	yes	characteristic
6	C₂₇×C₁₂₇	C₉	1	1	yes	characteristic
7	C₃×C₁₂₇⋊C₃	C₂₇	1	1	yes	characteristic
8	C₉×C₁₂₇	C₃×C₉	1	1	yes	characteristic
9	#11765917	C₂₇	1	2	yes	—
10	C₃×C₁₂₇	C₃×C₂₇	1	1	yes	characteristic
11	C₁₂₇⋊C₃	—	3	1	no	—
12	C₈₁⋊C₃	—	127	1	no	maximal, Sylow
13	C₁₂₇	C₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
14	C₃×C₂₇	—	127	1	no	—
15	C₈₁	—	127	3	no	—
16	C₃×C₉	—	127	1	no	—
17	C₂₇	—	127	1	no	—
18	C₂₇	—	127	1	no	—
19	C₂₇	#11765919	1	1	yes	characteristic
20	C₃²	—	127	1	no	—
21	C₉	—	127	2	no	—
22	C₉	C₃×#11765919	1	1	yes	characteristic
23	C₃	—	381	1	no	—
24	C₃	(C₁₂₇⋊C₃)⋊C₂₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #23779863	C₃	semidirect
13. C₁₂₇	C₈₁⋊C₃	semidirect

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