Subgroups — #44524968

Order 30861.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779840	C₃	1	1	yes	maximal, characteristic
2	#23779840	C₃	1	1	yes	maximal, characteristic
3	#23779835	C₃	1	1	yes	maximal, characteristic
4	C₂₇⋊C₃×C₁₂₇	C₃	1	1	yes	maximal, characteristic
5	C₃×#11765917	—	3	1	no	—
6	#16812178	—	3	1	no	—
7	#16812178	C₉	1	3	yes	complemented
8	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
9	C₂₇×C₁₂₇	—	3	1	no	—
10	C₃²×C₁₂₇	3₋¹⁺²	1	1	yes	characteristic
11	C₉×C₁₂₇	C₃×C₉	1	1	yes	characteristic
12	C₉×C₁₂₇	3₋¹⁺²	1	1	yes	characteristic
13	C₉×C₁₂₇	3₋¹⁺²	1	1	yes	characteristic
14	#11765917	—	9	1	no	—
15	C₃×C₁₂₇	—	3	1	no	—
16	C₃×C₁₂₇	C₉⋊C₉	1	1	yes	characteristic
17	#6875	—	127	1	no	maximal, Sylow
18	C₁₂₇	#6875	1	1	yes	characteristic, complemented, Sylow
19	C₂₇⋊C₃	—	127	1	no	—
20	C₂₇⋊C₃	—	127	1	no	—
21	C₂₇⋊C₃	C₁₂₇⋊C₃	1	1	yes	characteristic
22	C₉⋊C₉	—	127	1	no	—
23	C₃×C₉	—	381	1	no	—
24	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
25	C₂₇	—	3	1	no	—
26	C₂₇	—	381	1	no	—
27	C₂₇	—	127	3	no	—
28	C₃²	#16812182	1	1	yes	characteristic
29	C₉	—	1143	1	no	—
30	C₉	C₉×C₁₂₇⋊C₃	1	1	yes	characteristic
31	C₉	#16812183	1	1	yes	characteristic
32	C₉	#16812184	1	1	yes	characteristic
33	C₃	—	3	1	no	—
34	C₃	#23779833	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. #16812178	C₉	semidirect
18. C₁₂₇	#6875	semidirect

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