Subgroups — C₉×#16812178 #44524935

Order 30861.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812178	C₃	1	3	yes	maximal
2	C₉²×C₁₂₇	C₃	1	1	yes	maximal, characteristic
3	#16812178	C₉	1	9	yes	direct product factor
4	C₃×C₉×C₁₂₇	C₉	1	3	yes	—
5	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
6	C₃²×C₁₂₇	C₃×C₉	1	1	yes	characteristic
7	C₉×C₁₂₇	C₂₇	1	9	yes	complemented
8	C₉×C₁₂₇	C₃×C₉	1	3	yes	—
9	C₃×C₁₂₇	C₉²	1	1	yes	characteristic
10	C₃×C₁₂₇	C₃×C₂₇	1	3	yes	—
11	C₉×C₂₇	—	127	1	no	maximal, Sylow
12	C₁₂₇	C₉×C₂₇	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₂₇	—	127	3	no	—
14	C₉²	C₁₂₇⋊C₃	1	1	yes	characteristic
15	C₃×C₉	#11765917	1	3	yes	—
16	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
17	C₂₇	—	127	9	no	—
18	C₃²	C₃×#11765917	1	1	yes	characteristic
19	C₉	#16812178	1	9	yes	direct product factor
20	C₉	C₉×C₁₂₇⋊C₃	1	3	yes	—
21	C₃	C₉×#11765917	1	1	yes	characteristic
22	C₃	C₃×#16812178	1	3	yes	—

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.