Subgroups — #13090672

Order 1458.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624569	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×#4169	—	3	4	no	maximal
3	#92197	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃²⋊C₉	D₃	1	4	yes	—
5	#6855	—	2	4	no	—
6	#6855	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃²×C₃⋊D₃	—	9	1	no	—
8	C₃×C₃⋊D₉	—	3	4	no	—
9	#4169	—	3	12	no	—
10	C₃⁴	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₉	—	2	4	no	—
12	C₃²×C₉	C₃×D₃	1	4	yes	—
13	C₃²⋊C₉	—	3	12	no	—
14	C₃×C₃⋊D₃	—	9	3	no	—
15	C₃×C₃⋊D₃	—	9	1	no	—
16	C₃²×D₃	—	27	4	no	—
17	C₃⋊D₉	—	3	4	no	—
18	C₃×D₉	—	27	4	no	—
19	C₃³	—	3	4	no	—
20	C₃³	—	6	4	no	—
21	C₃³	#272	1	3	yes	—
22	C₃³	C₃×C₃⋊D₃	1	1	yes	characteristic
23	C₃×C₉	—	3	4	no	—
24	C₃×C₉	—	3	4	no	—
25	C₃×C₉	—	6	4	no	—
26	C₃×C₉	—	6	8	no	—
27	C₃×C₉	—	6	4	no	—
28	C₃×C₉	—	6	4	no	—
29	C₂×C₃²	—	81	1	no	—
30	C₃⋊D₃	—	9	1	no	—
31	C₃×D₃	—	27	12	no	—
32	C₃×D₃	—	27	4	no	—
33	D₉	—	27	4	no	—
34	C₃²	—	2	4	no	—
35	C₃²	—	3	12	no	—
36	C₃²	—	9	1	no	—
37	C₃²	—	18	4	no	—
38	C₃²	C₃×#272	1	1	yes	characteristic
39	C₃²	#4207	1	4	yes	—
40	C₉	—	9	4	no	—
41	C₉	—	18	4	no	—
42	C₂×C₃	—	81	3	no	—
43	C₂×C₃	—	81	1	no	—
44	D₃	—	27	4	no	—
45	C₃	—	2	4	no	—
46	C₃	—	9	3	no	—
47	C₃	#92304	1	4	yes	—
48	C₃	#92312	1	1	yes	characteristic
49	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#92312
commutator, cosocle, hypocenter	#6855	C₂×C₃
Frattini, socle	C₃³	C₃×C₃⋊D₃
Fitting	#10624569	C₂
LCS	G ▷ #6855
UCS	C₁ ◁ C₃

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.