Subgroups — Dic₃×D₉ #6190

Order 216.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×Dic₃	—	3	1	no	maximal
5	C₄×D₉	—	3	1	no	maximal
6	C₂×C₃×C₉	C₂²	1	1	yes	characteristic
7	C₃×D₉	C₄	1	2	yes	complemented
8	C₂×C₃×D₃	—	3	1	no	—
9	C₃⋊Dic₃	—	3	1	no	—
10	C₃×Dic₃	D₃	1	1	yes	characteristic
11	C₂×D₉	D₃	1	1	yes	characteristic
12	C₄×C₉	—	3	1	no	—
13	Dic₉	—	3	1	no	—
14	Dic₉	—	6	1	no	—
15	C₃×C₉	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂×Dic₃	—	9	1	no	—
17	C₄×D₃	—	9	1	no	—
18	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
19	C₃×D₃	—	3	2	no	—
20	C₂×C₉	—	2	1	no	—
21	C₂×C₉	C₂×D₃	1	1	yes	characteristic
22	D₉	Dic₃	1	2	yes	direct product factor
23	C₂²×C₃	—	9	1	no	—
24	C₂×D₃	—	3	1	no	—
25	C₃×C₄	—	3	1	no	—
26	Dic₃	—	9	1	no	—
27	Dic₃	—	9	1	no	—
28	Dic₃	—	18	1	no	—
29	Dic₃	D₉	1	1	yes	characteristic, direct product factor
30	C₃²	C₄×D₃	1	1	yes	characteristic
31	C₉	—	2	1	no	—
32	C₉	C₂×Dic₃	1	1	yes	characteristic, complemented
33	C₂×C₄	—	27	1	no	Sylow
34	C₂×C₃	—	2	1	no	—
35	C₂×C₃	—	9	2	no	—
36	C₂×C₃	C₂×D₉	1	1	yes	characteristic
37	C₂×C₃	D₃²	1	1	yes	characteristic
38	D₃	—	3	2	no	—
39	C₂²	—	9	1	no	—
40	C₄	—	3	1	no	—
41	C₄	—	27	1	no	—
42	C₃	—	2	1	no	—
43	C₃	C₄×D₉	1	1	yes	characteristic, complemented
44	C₃	D₃×Dic₃	1	1	yes	characteristic
45	C₂	—	9	2	no	—
46	C₂	D₃×D₉	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.