Subgroups — #40997012

Order 26487.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22579529	C₃	1	3	yes	maximal, complemented
2	#22579524	C₃	1	1	yes	maximal, characteristic
3	#15668885	C₉	1	2	yes	—
4	#15668885	C₃²	1	1	yes	characteristic
5	C₉×C₁₀₉⋊C₃	C₉	1	1	yes	characteristic
6	C₃×C₁₀₉⋊C₃	C₂₇	1	1	yes	characteristic
7	C₉×C₁₀₉	C₂₇	1	1	yes	characteristic
8	#11758279	C₂₇	1	1	yes	characteristic
9	#11758279	C₃×C₉	1	1	yes	characteristic
10	C₃×C₁₀₉	C₃×C₂₇	1	1	yes	characteristic
11	C₁₀₉⋊C₃	—	3	1	no	—
12	C₈₁⋊C₃	—	109	1	no	maximal, Sylow
13	C₁₀₉	C₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
14	C₃×C₂₇	—	109	1	no	—
15	C₈₁	—	109	3	no	—
16	C₃×C₉	—	109	1	no	—
17	C₂₇	—	109	2	no	—
18	C₂₇	—	109	1	no	—
19	C₃²	—	109	1	no	—
20	C₉	—	109	1	no	—
21	C₉	—	109	1	no	—
22	C₉	#15668887	1	1	yes	characteristic
23	C₃	—	327	1	no	—
24	C₃	C₃×#15668887	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #22579529	C₃	semidirect
13. C₁₀₉	C₈₁⋊C₃	semidirect

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