Subgroups — #66316

Order 324.

53 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃⋊Dic₃	—	3	1	no	maximal
3	C₃⋊Dic₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²⋊C₉	C₄	1	1	yes	characteristic, complemented, Sylow
5	C₂×C₃³	D₃	1	1	yes	characteristic
6	C₂×C₃×C₉	—	2	1	no	—
7	C₂×C₃×C₉	C₂×C₃	1	1	yes	characteristic
8	C₃⋊Dic₃	—	3	1	no	—
9	C₃×Dic₃	—	9	1	no	—
10	C₃×Dic₃	—	9	2	no	—
11	C₃×Dic₃	—	9	1	no	—
12	Dic₉	—	9	1	no	—
13	C₃³	Dic₃	1	1	yes	characteristic
14	C₃×C₉	—	2	1	no	—
15	C₃×C₉	C₃×C₄	1	1	yes	characteristic, complemented
16	C₂×C₃²	—	2	1	no	—
17	C₂×C₃²	—	3	1	no	—
18	C₂×C₃²	—	3	2	no	—
19	C₂×C₃²	D₉	1	1	yes	characteristic
20	C₂×C₃²	C₃×D₃	1	1	yes	characteristic
21	C₂×C₉	—	3	1	no	—
22	C₂×C₉	—	6	1	no	—
23	C₃×C₄	—	27	1	no	—
24	Dic₃	—	9	1	no	—
25	Dic₃	—	9	1	no	—
26	Dic₃	—	9	2	no	—
27	C₃²	—	2	1	no	—
28	C₃²	—	3	1	no	—
29	C₃²	—	3	2	no	—
30	C₃²	Dic₉	1	1	yes	characteristic, complemented
31	C₃²	C₃×Dic₃	1	1	yes	characteristic
32	C₉	—	3	1	no	—
33	C₉	—	6	1	no	—
34	C₂×C₃	—	3	1	no	—
35	C₂×C₃	—	6	1	no	—
36	C₂×C₃	C₃×D₉	1	1	yes	characteristic
37	C₂×C₃	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
38	C₂×C₃	AGL(1,ℤ/9)	1	2	yes	—
39	C₄	—	27	1	no	Sylow
40	C₃	—	3	1	no	—
41	C₃	—	6	1	no	—
42	C₃	C₃×Dic₉	1	1	yes	characteristic
43	C₃	(C₃⋊Dic₃)⋊C₃	1	1	yes	characteristic
44	C₃	3₋¹⁺²⋊C₄	1	2	yes	—
45	C₂	#4169	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.