Subgroups — C₃²×#13095301 #28355718

Order 13851.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095301	C₃	1	12	yes	maximal, direct product factor
2	C₃²×C₁₉×C₂₇	C₃	1	1	yes	maximal, characteristic
3	#13095301	C₃²	1	9	yes	direct product factor
4	C₃²×C₉×C₁₉	C₉	1	1	yes	characteristic
5	C₃×C₁₉×C₂₇	C₉	1	8	yes	—
6	C₃×C₁₉×C₂₇	C₃²	1	4	yes	—
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	C₁₉×C₂₇	C₃×C₉	1	8	yes	—
12	C₁₉×C₂₇	C₃³	1	1	yes	characteristic
13	C₃²×C₂₇	C₁₉⋊C₃	1	1	yes	characteristic
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	#4294	1	1	yes	characteristic
20	C₃×C₂₇	#4294	1	8	yes	—
21	C₃×C₂₇	C₃×C₁₉⋊C₃	1	4	yes	—
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	#10587018	1	1	yes	characteristic
26	C₃×C₉	#10587018	1	8	yes	—
27	C₃×C₉	C₃×#4294	1	4	yes	—
28	C₂₇	C₃×#4294	1	8	yes	—
29	C₂₇	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
30	C₁₉	C₃²×C₈₁	1	1	yes	characteristic, complemented, Sylow
31	C₃²	#13095301	1	9	yes	direct product factor
32	C₃²	C₃×#10587018	1	4	yes	—
33	C₉	C₃×#10587018	1	8	yes	—
34	C₉	C₃²×#4294	1	1	yes	characteristic
35	C₃	C₃×#13095301	1	12	yes	direct product factor
36	C₃	C₃²×#10587018	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.