Subgroups — C₃×D₄×C₉ #6239

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	2	yes	maximal, complemented
2	C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₄	C₃	1	1	yes	maximal, characteristic
4	D₄×C₉	C₃	1	3	yes	maximal, direct product factor
5	C₂×C₃×C₉	—	2	2	no	—
6	C₂×C₃×C₉	C₂²	1	1	yes	characteristic
7	C₂²×C₃²	C₂×C₃	1	2	yes	—
8	C₃²×C₄	C₂×C₃	1	1	yes	characteristic
9	C₂²×C₉	C₂×C₃	1	6	yes	complemented
10	C₄×C₉	C₂×C₃	1	3	yes	complemented
11	C₃×C₉	D₄	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×D₄	C₉	1	3	yes	direct product factor
13	C₃×D₄	C₃²	1	1	yes	characteristic
14	C₂×C₃²	—	2	2	no	—
15	C₂×C₃²	C₂²×C₃	1	1	yes	characteristic
16	C₂×C₉	—	2	6	no	—
17	C₂×C₉	C₂²×C₃	1	3	yes	—
18	C₂²×C₃	C₂×C₉	1	6	yes	complemented
19	C₂²×C₃	C₂×C₃²	1	2	yes	—
20	C₃×C₄	C₂×C₉	1	3	yes	complemented
21	C₃×C₄	C₂×C₃²	1	1	yes	characteristic
22	C₃²	C₃×D₄	1	1	yes	characteristic
23	C₉	C₃×D₄	1	3	yes	direct product factor
24	D₄	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃	—	2	6	no	—
26	C₂×C₃	—	2	2	no	—
27	C₂×C₃	C₂²×C₉	1	3	yes	—
28	C₂×C₃	C₂²×C₃²	1	1	yes	characteristic
29	C₂²	C₂×C₃×C₉	1	2	yes	complemented
30	C₄	C₂×C₃×C₉	1	1	yes	characteristic, complemented
31	C₃	D₄×C₉	1	3	yes	direct product factor
32	C₃	C₃²×D₄	1	1	yes	characteristic
33	C₂	—	2	2	no	—
34	C₂	C₂²×C₃×C₉	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.