Subgroups — (C₃⋊D₉)⋊C₄ #6191

Order 216.

58 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	C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#624	—	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	—	3	1	no	—
12	C₂×D₉	—	6	1	no	—
13	C₄×C₉	—	3	1	no	—
14	Dic₉	D₃	1	1	yes	characteristic, complemented
15	C₃×C₉	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₄×D₃	—	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	—	3	2	no	—
23	D₉	—	6	2	no	—
24	C₂×D₃	—	9	1	no	—
25	C₂×D₃	—	9	1	no	—
26	C₂×D₃	—	18	1	no	—
27	C₃×C₄	—	3	1	no	—
28	C₃×C₄	—	9	1	no	—
29	Dic₃	—	3	1	no	—
30	Dic₃	D₉	1	1	yes	characteristic, complemented
31	C₃²	C₄×D₃	1	1	yes	characteristic
32	C₉	—	2	1	no	—
33	C₉	C₄×D₃	1	1	yes	characteristic, complemented
34	C₂×C₄	—	27	1	no	Sylow
35	C₂×C₃	—	2	1	no	—
36	C₂×C₃	C₂×D₉	1	1	yes	characteristic
37	C₂×C₃	D₃²	1	1	yes	characteristic
38	D₃	—	9	2	no	—
39	D₃	—	9	2	no	—
40	D₃	—	18	2	no	—
41	C₂²	—	27	1	no	—
42	C₄	—	3	1	no	—
43	C₄	—	9	1	no	—
44	C₃	—	2	1	no	—
45	C₃	C₄×D₉	1	1	yes	characteristic, complemented
46	C₃	#624	1	1	yes	characteristic
47	C₂	—	27	2	no	—
48	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.