Subgroups — #30685264

Order 17091.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₁₁⋊C₂₇	C₃	1	3	yes	maximal, complemented
2	C₃×C₉×C₂₁₁	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₂₁₁	C₉	1	1	yes	characteristic
4	C₉×C₂₁₁	C₉	1	2	yes	—
5	C₉×C₂₁₁	C₃²	1	1	yes	characteristic
6	C₃×C₂₁₁	—	3	1	no	—
7	C₃×C₂₁₁	C₃×C₉	1	1	yes	characteristic
8	C₂₁₁	C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
9	C₂₇⋊C₃	—	211	1	no	maximal, Sylow
10	C₃×C₉	C₂₁₁⋊C₃	1	1	yes	characteristic
11	C₂₇	—	211	3	no	—
12	C₃²	C₂₁₁⋊C₉	1	1	yes	characteristic
13	C₉	C₂₁₁⋊C₉	1	2	yes	—
14	C₉	C₃×C₂₁₁⋊C₃	1	1	yes	characteristic
15	C₃	—	3	1	no	—
16	C₃	C₃×C₂₁₁⋊C₉	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. C₂₁₁⋊C₂₇	C₃	semidirect
8. C₂₁₁	C₂₇⋊C₃	semidirect

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