Subgroups — C₃×#23779870 #44525201

Order 30861.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779870	C₃	1	9	yes	maximal, direct product factor
2	C₃×#16812186	C₃	1	3	yes	maximal, complemented
3	C₃²×#11765917	C₃	1	1	yes	maximal, characteristic
4	#16812186	C₃²	1	9	yes	complemented
5	C₃×#11765917	C₉	1	6	yes	—
6	C₃×#11765917	C₉	1	2	yes	—
7	C₃×#11765917	C₃²	1	1	yes	characteristic
8	C₃×#11765917	C₃²	1	3	yes	—
9	C₃³×C₁₂₇	C₉	1	1	yes	characteristic
10	C₃²×C₁₂₇	—	3	3	no	—
11	C₃²×C₁₂₇	C₃×C₉	1	3	yes	—
12	C₃²×C₁₂₇	C₃×C₉	1	1	yes	characteristic
13	#11765917	C₃×C₉	1	2	yes	—
14	#11765917	C₃×C₉	1	6	yes	—
15	#11765917	C₃³	1	1	yes	characteristic
16	C₃×C₁₂₇	—	3	3	no	—
17	C₃×C₁₂₇	C₂₇⋊C₃	1	3	yes	complemented
18	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
19	C₃×C₂₇⋊C₃	—	127	1	no	maximal, Sylow
20	C₁₂₇	C₃×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₃²×C₉	—	127	1	no	—
22	C₂₇⋊C₃	—	127	9	no	—
23	C₃×C₂₇	—	127	3	no	—
24	C₃³	#11765919	1	1	yes	characteristic
25	C₃×C₉	—	127	6	no	—
26	C₃×C₉	—	127	3	no	—
27	C₃×C₉	—	127	2	no	—
28	C₃×C₉	—	127	1	no	—
29	C₂₇	—	127	9	no	—
30	C₃²	—	3	3	no	—
31	C₃²	C₃×#11765919	1	3	yes	—
32	C₃²	C₃×#11765919	1	1	yes	characteristic
33	C₉	—	127	1	no	—
34	C₉	—	127	2	no	—
35	C₉	—	127	6	no	—
36	C₃	—	3	3	no	—
37	C₃	#23779870	1	3	yes	direct product factor
38	C₃	C₃²×#11765919	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.