Subgroups — C₃³×#11765917 #44525139

Order 30861.

792 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11765917	C₃	1	39	yes	maximal, direct product factor
2	C₃⁴×C₁₂₇	C₃	1	1	yes	maximal, characteristic
3	C₃×#11765917	C₃²	1	117	yes	direct product factor
4	C₃³×C₁₂₇	C₉	1	27	yes	complemented
5	C₃³×C₁₂₇	C₃²	1	13	yes	—
6	C₃²×C₁₂₇	C₃×C₉	1	117	yes	complemented
7	C₃²×C₁₂₇	C₃³	1	13	yes	—
8	#11765917	C₃³	1	27	yes	direct product factor
9	C₃×C₁₂₇	C₃²×C₉	1	39	yes	complemented
10	C₃×C₁₂₇	C₃⁴	1	1	yes	characteristic
11	C₃³×C₉	—	127	1	no	maximal, Sylow
12	C₁₂₇	C₃³×C₉	1	1	yes	characteristic, complemented, Sylow
13	C₃⁴	C₁₂₇⋊C₃	1	1	yes	characteristic
14	C₃²×C₉	—	127	39	no	—
15	C₃³	#11765917	1	27	yes	direct product factor
16	C₃³	C₃×C₁₂₇⋊C₃	1	13	yes	—
17	C₃×C₉	—	127	117	no	—
18	C₃²	C₃×#11765917	1	117	yes	direct product factor
19	C₃²	C₃²×C₁₂₇⋊C₃	1	13	yes	—
20	C₉	—	127	27	no	—
21	C₃	C₃²×#11765917	1	39	yes	direct product factor
22	C₃	C₃³×C₁₂₇⋊C₃	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.