Subgroups — #30685259

Order 17091.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₁₁⋊C₉	C₃	1	3	yes	maximal
2	C₃×C₉×C₂₁₁	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₂₁₁	C₃²	1	1	yes	characteristic
4	C₉×C₂₁₁	C₉	1	3	yes	complemented
5	C₂₁₁⋊C₉	—	3	3	no	—
6	C₃×C₂₁₁	C₃×C₉	1	1	yes	characteristic
7	C₃×C₂₁₁	3₋¹⁺²	1	3	yes	—
8	C₂₁₁	C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
9	C₉⋊C₉	—	211	1	no	maximal, Sylow
10	C₃×C₉	—	211	3	no	—
11	C₃×C₉	C₂₁₁⋊C₃	1	1	yes	characteristic
12	C₃²	C₃×C₂₁₁⋊C₃	1	1	yes	characteristic
13	C₉	—	633	3	no	—
14	C₉	C₂₁₁⋊C₉	1	3	yes	complemented
15	C₃	C₃×C₂₁₁⋊C₉	1	1	yes	characteristic
16	C₃	#19152731	1	3	yes	—

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.