Subgroups — #44525183

Order 30861.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779871	C₃	1	2	yes	maximal
2	#23779866	C₃	1	1	yes	maximal, characteristic
3	#23779839	C₃	1	1	yes	maximal, characteristic
4	C₃×#11765919	—	3	1	no	—
5	#16812186	—	3	2	no	—
6	C₉×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
7	#16812178	C₉	1	2	yes	complemented
8	C₂₇×C₁₂₇	C₉	1	1	yes	characteristic, complemented
9	C₃×C₁₂₇⋊C₃	3₋¹⁺²	1	1	yes	characteristic
10	#11765919	—	9	1	no	—
11	C₉×C₁₂₇	C₃×C₉	1	1	yes	characteristic
12	#11765917	3₋¹⁺²	1	2	yes	—
13	C₃×C₁₂₇	C₉⋊C₉	1	1	yes	characteristic
14	C₁₂₇⋊C₃	—	3	1	no	—
15	#6875	—	127	1	no	maximal, Sylow
16	C₁₂₇	#6875	1	1	yes	characteristic, complemented, Sylow
17	C₂₇⋊C₃	—	127	2	no	—
18	C₂₇⋊C₃	—	127	1	no	—
19	C₉⋊C₉	—	127	1	no	—
20	C₃×C₉	—	381	1	no	—
21	C₃×C₉	—	127	1	no	—
22	C₂₇	—	381	2	no	—
23	C₂₇	—	127	2	no	—
24	C₂₇	#11765919	1	1	yes	characteristic, complemented
25	C₃²	—	127	1	no	—
26	C₉	—	1143	1	no	—
27	C₉	—	127	2	no	—
28	C₉	C₃×#11765919	1	1	yes	characteristic
29	C₃	—	381	1	no	—
30	C₃	#23779866	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.