Subgroups — #30685262

Order 17091.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₁₁⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₂₁₁⋊C₂₇	C₃	1	2	yes	maximal, complemented
3	C₂₇×C₂₁₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₂₁₁⋊C₃	C₉	1	1	yes	characteristic
5	C₉×C₂₁₁	C₃²	1	1	yes	characteristic
6	C₂₁₁⋊C₉	C₉	1	2	yes	—
7	C₃×C₂₁₁	C₃×C₉	1	1	yes	characteristic
8	C₂₁₁⋊C₃	—	3	1	no	—
9	C₂₁₁	C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
10	C₂₇⋊C₃	—	211	1	no	maximal, Sylow
11	C₃×C₉	—	211	1	no	—
12	C₂₇	—	211	2	no	—
13	C₂₇	C₂₁₁⋊C₃	1	1	yes	characteristic, complemented
14	C₃²	—	211	1	no	—
15	C₉	—	211	2	no	—
16	C₉	C₃×C₂₁₁⋊C₃	1	1	yes	characteristic
17	C₃	—	633	1	no	—
18	C₃	C₉×C₂₁₁⋊C₃	1	1	yes	characteristic

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

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