Subgroups — #21419257

Order 7533.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₇×C₃₁⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃₁⋊C₈₁	C₃	1	2	yes	maximal, complemented
3	C₃₁×C₈₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₉×C₃₁⋊C₃	C₉	1	1	yes	characteristic
5	C₂₇×C₃₁	C₃²	1	1	yes	characteristic
6	C₃₁⋊C₂₇	C₉	1	2	yes	—
7	C₃×C₃₁⋊C₃	C₂₇	1	1	yes	characteristic
8	C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
9	C₃₁⋊C₉	C₂₇	1	2	yes	—
10	C₈₁⋊C₃	—	31	1	no	maximal, Sylow
11	C₃×C₃₁	C₃×C₂₇	1	1	yes	characteristic
12	C₃₁⋊C₃	—	3	1	no	—
13	C₃×C₂₇	—	31	1	no	—
14	C₈₁	—	31	2	no	—
15	C₈₁	C₃₁⋊C₃	1	1	yes	characteristic, complemented
16	C₃₁	C₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₉	—	31	1	no	—
18	C₂₇	—	31	2	no	—
19	C₂₇	C₃×C₃₁⋊C₃	1	1	yes	characteristic
20	C₃²	—	31	1	no	—
21	C₉	—	31	2	no	—
22	C₉	C₉×C₃₁⋊C₃	1	1	yes	characteristic
23	C₃	—	93	1	no	—
24	C₃	C₂₇×C₃₁⋊C₃	1	1	yes	characteristic

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