Subgroups — C₃²×#13095335 #28357031

Order 13851.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095335	C₃	1	12	yes	maximal, direct product factor
2	C₃²×#10587018	C₃	1	1	yes	maximal, characteristic
3	#13095335	C₃²	1	9	yes	direct product factor
4	C₃×#10587018	C₉	1	8	yes	—
5	C₃×#10587018	C₃²	1	4	yes	—
6	C₃²×C₉×C₁₉	C₉	1	1	yes	characteristic
7	C₃²×C₈₁	—	19	1	no	maximal, Sylow
8	C₃³×C₁₉	C₂₇	1	1	yes	characteristic
9	C₃×C₉×C₁₉	C₂₇	1	8	yes	—
10	C₃×C₉×C₁₉	C₃×C₉	1	4	yes	—
11	#10587018	C₃×C₉	1	8	yes	—
12	#10587018	C₃³	1	1	yes	characteristic
13	C₃²×C₂₇	—	19	1	no	—
14	C₃×C₈₁	—	19	12	no	—
15	C₃²×C₁₉	C₈₁	1	9	yes	complemented
16	C₃²×C₁₉	C₃×C₂₇	1	4	yes	—
17	C₉×C₁₉	C₃×C₂₇	1	8	yes	—
18	C₉×C₁₉	C₃²×C₉	1	1	yes	characteristic
19	C₃²×C₉	#4296	1	1	yes	characteristic
20	C₃×C₂₇	—	19	8	no	—
21	C₃×C₂₇	—	19	4	no	—
22	C₈₁	—	19	9	no	—
23	C₃×C₁₉	C₃×C₈₁	1	12	yes	complemented
24	C₃×C₁₉	C₃²×C₂₇	1	1	yes	characteristic
25	C₃³	#10587020	1	1	yes	characteristic
26	C₃×C₉	#10587020	1	8	yes	—
27	C₃×C₉	C₃×#4296	1	4	yes	—
28	C₂₇	—	19	8	no	—
29	C₂₇	—	19	1	no	—
30	C₁₉	C₃²×C₈₁	1	1	yes	characteristic, complemented, Sylow
31	C₃²	#13095335	1	9	yes	direct product factor
32	C₃²	C₃×#10587020	1	4	yes	—
33	C₉	C₃×#10587020	1	8	yes	—
34	C₉	C₃²×#4296	1	1	yes	characteristic
35	C₃	C₃×#13095335	1	12	yes	direct product factor
36	C₃	C₃²×#10587020	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.