Subgroups — #44524974

Order 30861.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779829	C₃	1	3	yes	maximal, complemented
2	C₃×C₂₇×C₁₂₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₉×C₁₂₇	C₉	1	1	yes	characteristic
4	C₂₇×C₁₂₇	C₉	1	2	yes	—
5	C₂₇×C₁₂₇	C₃²	1	1	yes	characteristic
6	C₃²×C₁₂₇	C₂₇	1	1	yes	characteristic
7	C₉×C₁₂₇	C₂₇	1	2	yes	—
8	C₉×C₁₂₇	C₃×C₉	1	1	yes	characteristic
9	C₃×C₁₂₇	—	3	1	no	—
10	C₃×C₁₂₇	C₃×C₂₇	1	1	yes	characteristic
11	C₈₁⋊C₃	—	127	1	no	maximal, Sylow
12	C₁₂₇	C₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₂₇	C₁₂₇⋊C₃	1	1	yes	characteristic
14	C₈₁	—	127	3	no	—
15	C₃×C₉	#11765917	1	1	yes	characteristic
16	C₂₇	#11765917	1	2	yes	—
17	C₂₇	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
18	C₃²	#16812178	1	1	yes	characteristic
19	C₉	#16812178	1	2	yes	—
20	C₉	C₃×#11765917	1	1	yes	characteristic
21	C₃	—	3	1	no	—
22	C₃	C₃×#16812178	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #23779829	C₃	semidirect
12. C₁₂₇	C₈₁⋊C₃	semidirect

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