Subgroups — #44524992

Order 30861.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779850	C₃	1	3	yes	maximal
2	C₉⋊C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic
3	#16812184	—	3	3	no	—
4	C₃×C₉×C₁₂₇	—	3	1	no	—
5	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
6	C₃²×C₁₂₇	H(3,𝔽₃)	1	1	yes	characteristic
7	C₉×C₁₂₇	—	3	1	no	—
8	C₉×C₁₂₇	—	9	1	no	—
9	#11765917	—	9	3	no	—
10	C₃×C₁₂₇	—	3	1	no	—
11	C₃×C₁₂₇	#732	1	1	yes	characteristic
12	#6882	—	127	1	no	maximal, Sylow
13	C₁₂₇	#6882	1	1	yes	characteristic, complemented, Sylow
14	#733	—	127	3	no	—
15	C₉⋊C₉	C₁₂₇⋊C₃	1	1	yes	characteristic
16	3₋¹⁺²	—	381	3	no	—
17	C₃×C₉	—	3	1	no	—
18	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
19	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic
20	C₉	—	3	1	no	—
21	C₉	—	9	1	no	—
22	C₉	—	1143	3	no	—
23	C₃	—	3	1	no	—
24	C₃	#23779848	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. C₁₂₇	#6882	semidirect

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