Subgroups — C₂×C₃⋊Dic₉ #6232

Order 216.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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