Subgroups — #44524981

Order 30861.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779848	C₃	1	3	yes	maximal, complemented
2	C₉²×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²⋊(C₁₂₇⋊C₃)	—	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	C₃×C₁₂₇⋊C₃	—	9	3	no	—
8	C₉×C₁₂₇	—	3	3	no	—
9	C₉×C₁₂₇	—	3	1	no	—
10	C₃×C₁₂₇	—	3	1	no	—
11	C₃×C₁₂₇	#732	1	1	yes	characteristic
12	C₁₂₇⋊C₃	—	27	3	no	—
13	#6879	—	127	1	no	maximal, Sylow
14	C₁₂₇	#6879	1	1	yes	characteristic, complemented, Sylow
15	#732	—	127	3	no	—
16	C₉²	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
17	H(3,𝔽₃)	—	381	3	no	—
18	C₃×C₉	—	3	1	no	—
19	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
20	C₃²	—	1143	3	no	—
21	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic
22	C₉	—	3	3	no	—
23	C₉	—	3	1	no	—
24	C₃	—	3	1	no	—
25	C₃	—	3429	3	no	—
26	C₃	#23779848	1	1	yes	characteristic

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.