Subgroups — #92158

Order 486.

69 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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.