Subgroups — C₃²×#16812178 #44525081

Order 30861.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812178	C₃	1	12	yes	maximal, direct product factor
2	C₃²×C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic
3	#16812178	C₃²	1	9	yes	direct product factor
4	C₃³×C₁₂₇	C₉	1	1	yes	characteristic
5	C₃×C₉×C₁₂₇	C₉	1	8	yes	—
6	C₃×C₉×C₁₂₇	C₃²	1	4	yes	—
7	C₃²×C₁₂₇	C₂₇	1	9	yes	complemented
8	C₃²×C₁₂₇	C₃×C₉	1	4	yes	—
9	C₉×C₁₂₇	C₃×C₉	1	8	yes	—
10	C₉×C₁₂₇	C₃³	1	1	yes	characteristic
11	C₃×C₁₂₇	C₃×C₂₇	1	12	yes	complemented
12	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
13	C₃²×C₂₇	—	127	1	no	maximal, Sylow
14	C₁₂₇	C₃²×C₂₇	1	1	yes	characteristic, complemented, Sylow
15	C₃²×C₉	C₁₂₇⋊C₃	1	1	yes	characteristic
16	C₃×C₂₇	—	127	12	no	—
17	C₃³	#11765917	1	1	yes	characteristic
18	C₃×C₉	#11765917	1	8	yes	—
19	C₃×C₉	C₃×C₁₂₇⋊C₃	1	4	yes	—
20	C₂₇	—	127	9	no	—
21	C₃²	#16812178	1	9	yes	direct product factor
22	C₃²	C₃×#11765917	1	4	yes	—
23	C₉	C₃×#11765917	1	8	yes	—
24	C₉	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
25	C₃	C₃×#16812178	1	12	yes	direct product factor
26	C₃	C₃²×#11765917	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.