Subgroups — C₉×C₃⋊Dic₃ #66405

Order 324.

86 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	C₃	1	1	yes	maximal, characteristic
3	C₉×Dic₃	—	3	4	no	maximal
4	C₃²×C₉	C₄	1	1	yes	characteristic, complemented, Sylow
5	C₂×C₃³	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₉	—	2	4	no	—
7	C₂×C₃×C₉	D₃	1	4	yes	—
8	C₃⋊Dic₃	C₉	1	1	yes	characteristic, direct product factor
9	C₃×Dic₃	—	3	4	no	—
10	C₄×C₉	—	9	1	no	—
11	C₃³	C₃×C₄	1	1	yes	characteristic
12	C₃×C₉	—	2	4	no	—
13	C₃×C₉	Dic₃	1	4	yes	complemented
14	C₂×C₃²	—	2	4	no	—
15	C₂×C₃²	C₂×C₉	1	1	yes	characteristic
16	C₂×C₃²	C₃×D₃	1	4	yes	—
17	C₂×C₉	—	2	4	no	—
18	C₂×C₉	C₃⋊D₃	1	1	yes	characteristic
19	C₃×C₄	—	9	1	no	—
20	Dic₃	—	3	4	no	—
21	C₃²	—	2	4	no	—
22	C₃²	C₄×C₉	1	1	yes	characteristic, complemented
23	C₃²	C₃×Dic₃	1	4	yes	—
24	C₉	—	2	4	no	—
25	C₉	C₃⋊Dic₃	1	1	yes	characteristic, direct product factor
26	C₂×C₃	—	2	4	no	—
27	C₂×C₃	D₃×C₉	1	4	yes	—
28	C₂×C₃	C₃×C₃⋊D₃	1	1	yes	characteristic
29	C₄	—	9	1	no	Sylow
30	C₃	—	2	4	no	—
31	C₃	C₉×Dic₃	1	4	yes	complemented
32	C₃	C₃×C₃⋊Dic₃	1	1	yes	characteristic
33	C₂	C₉×C₃⋊D₃	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.