Subgroups — C₃³×#10587020 #28357051

Order 13851.

1160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#10587020	C₃	1	39	yes	maximal, direct product factor
2	C₃³×#4294	C₃	1	1	yes	maximal, characteristic
3	C₃×#10587020	C₃²	1	117	yes	direct product factor
4	C₃²×#4294	C₉	1	26	yes	—
5	C₃²×#4294	C₃²	1	13	yes	—
6	C₃⁴×C₁₉	C₉	1	1	yes	characteristic
7	C₃³×C₂₇	—	19	1	no	maximal, Sylow
8	C₃³×C₁₉	C₂₇	1	27	yes	complemented
9	C₃³×C₁₉	C₃×C₉	1	13	yes	—
10	C₃×#4294	C₃×C₉	1	104	yes	—
11	C₃×#4294	C₃³	1	13	yes	—
12	#10587020	C₃³	1	27	yes	direct product factor
13	C₃³×C₉	—	19	1	no	—
14	C₃²×C₂₇	—	19	39	no	—
15	C₃²×C₁₉	C₃×C₂₇	1	117	yes	complemented
16	C₃²×C₁₉	C₃²×C₉	1	13	yes	—
17	#4294	C₃²×C₉	1	26	yes	—
18	#4294	C₃⁴	1	1	yes	characteristic
19	C₃⁴	#4296	1	1	yes	characteristic
20	C₃²×C₉	—	19	26	no	—
21	C₃²×C₉	—	19	13	no	—
22	C₃×C₂₇	—	19	117	no	—
23	C₃×C₁₉	C₃²×C₂₇	1	39	yes	complemented
24	C₃×C₁₉	C₃³×C₉	1	1	yes	characteristic
25	C₃³	#10587020	1	27	yes	direct product factor
26	C₃³	C₃×#4296	1	13	yes	—
27	C₃×C₉	—	19	104	no	—
28	C₃×C₉	—	19	13	no	—
29	C₂₇	—	19	27	no	—
30	C₁₉	C₃³×C₂₇	1	1	yes	characteristic, complemented, Sylow
31	C₃²	C₃×#10587020	1	117	yes	direct product factor
32	C₃²	C₃²×#4296	1	13	yes	—
33	C₉	—	19	1	no	—
34	C₉	—	19	26	no	—
35	C₃	C₃²×#10587020	1	39	yes	direct product factor
36	C₃	C₃³×#4296	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.