Subgroups — C₄×C₃⋊D₉ #6227

Order 216.

80 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×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₃⋊D₃	—	3	1	no	maximal
5	C₄×D₉	—	3	3	no	maximal
6	C₂×C₃×C₉	C₂²	1	1	yes	characteristic
7	C₃⋊D₉	C₄	1	2	yes	direct product factor
8	C₂×C₃⋊D₃	—	3	1	no	—
9	C₃²×C₄	D₃	1	1	yes	characteristic
10	C₃⋊Dic₃	—	3	1	no	—
11	C₂×D₉	—	3	3	no	—
12	C₄×C₉	D₃	1	3	yes	complemented
13	Dic₉	—	3	3	no	—
14	C₃×C₉	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
15	C₄×D₃	—	9	3	no	—
16	C₄×D₃	—	9	1	no	—
17	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
18	C₃⋊D₃	—	3	2	no	—
19	C₂×C₉	C₂×D₃	1	3	yes	—
20	D₉	—	3	6	no	—
21	C₂×D₃	—	9	3	no	—
22	C₂×D₃	—	9	1	no	—
23	C₃×C₄	D₉	1	3	yes	complemented
24	C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
25	Dic₃	—	9	3	no	—
26	Dic₃	—	9	1	no	—
27	C₃²	C₄×D₃	1	1	yes	characteristic
28	C₉	C₄×D₃	1	3	yes	complemented
29	C₂×C₄	—	27	1	no	Sylow
30	C₂×C₃	C₂×D₉	1	3	yes	—
31	C₂×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
32	D₃	—	9	6	no	—
33	D₃	—	9	2	no	—
34	C₂²	—	27	1	no	—
35	C₄	—	27	1	no	—
36	C₄	C₃⋊D₉	1	1	yes	characteristic, direct product factor
37	C₃	C₄×D₉	1	3	yes	complemented
38	C₃	C₄×C₃⋊D₃	1	1	yes	characteristic
39	C₂	—	27	2	no	—
40	C₂	C₂×C₃⋊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.