Subgroups — #13133492

Order 1701.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₂₇	C₃	1	1	yes	maximal, characteristic
2	C₇⋊C₈₁	C₃	1	3	yes	maximal, complemented
3	C₈₁⋊C₃	—	7	1	no	maximal, Sylow
4	C₃×C₇×C₉	C₉	1	1	yes	characteristic
5	C₇×C₂₇	C₉	1	2	yes	—
6	C₇×C₂₇	C₃²	1	1	yes	characteristic
7	C₃×C₂₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
8	C₈₁	—	7	3	no	—
9	C₃²×C₇	C₂₇	1	1	yes	characteristic
10	C₇×C₉	C₂₇	1	2	yes	—
11	C₇×C₉	C₃×C₉	1	1	yes	characteristic
12	C₃×C₉	C₇⋊C₉	1	1	yes	characteristic
13	C₂₇	C₇⋊C₉	1	2	yes	—
14	C₂₇	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₃×C₇	—	3	1	no	—
16	C₃×C₇	C₃×C₂₇	1	1	yes	characteristic
17	C₃²	C₇⋊C₂₇	1	1	yes	characteristic
18	C₉	C₇⋊C₂₇	1	2	yes	—
19	C₉	C₃×C₇⋊C₉	1	1	yes	characteristic
20	C₇	C₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₃	—	3	1	no	—
22	C₃	C₃×C₇⋊C₂₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₇⋊C₈₁	C₃	semidirect
20. C₇	C₈₁⋊C₃	semidirect

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