Subgroups — #44525126

Order 30861.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812184	C₃	1	3	yes	maximal
2	#23779850	C₃	1	9	yes	maximal, complemented
3	C₃×3₋¹⁺²×C₁₂₇	C₃	1	1	yes	maximal, characteristic
4	#16812184	—	3	6	no	—
5	#16812184	C₃²	1	9	yes	—
6	C₃×#11765917	—	3	3	no	—
7	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
8	3₋¹⁺²×C₁₂₇	—	3	3	no	—
9	C₃×C₉×C₁₂₇	C₃²	1	3	yes	—
10	C₃²×C₁₂₇	—	9	1	no	—
11	C₃²×C₁₂₇	H(3,𝔽₃)	1	3	yes	—
12	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
13	C₉×C₁₂₇	—	3	3	no	—
14	#11765917	—	3	9	no	—
15	C₃×C₁₂₇	—	3	3	no	—
16	C₃×C₁₂₇	—	3	1	no	—
17	C₃×C₁₂₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
18	#6912	—	127	1	no	maximal, Sylow
19	C₁₂₇	#6912	1	1	yes	characteristic, complemented, Sylow
20	C₃×3₋¹⁺²	—	127	3	no	—
21	C₃×3₋¹⁺²	C₁₂₇⋊C₃	1	1	yes	characteristic
22	#733	—	127	9	no	—
23	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
24	3₋¹⁺²	—	3	3	no	—
25	3₋¹⁺²	—	381	6	no	—
26	3₋¹⁺²	—	127	9	no	—
27	C₃×C₉	—	381	3	no	—
28	C₃×C₉	C₃×C₁₂₇⋊C₃	1	3	yes	—
29	C₃²	—	9	1	no	—
30	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	3	yes	—
31	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
32	C₉	—	3	3	no	—
33	C₉	—	381	9	no	—
34	C₃	—	3	3	no	—
35	C₃	—	3	1	no	—
36	C₃	C₃×C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #23779850	C₃	semidirect
19. C₁₂₇	#6912	semidirect

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