Subgroups — C₉×D₁₂ #6211

Order 216.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₉	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₂	C₃	1	1	yes	maximal, characteristic
4	D₄×C₉	—	3	1	no	maximal
5	C₂×C₃×C₉	C₂²	1	1	yes	characteristic
6	D₃×C₉	—	2	2	no	—
7	C₂×C₃×D₃	C₂×C₃	1	2	yes	—
8	C₃²×C₄	C₂×C₃	1	1	yes	characteristic
9	C₂²×C₉	—	3	2	no	—
10	C₄×C₉	—	2	1	no	—
11	C₄×C₉	D₃	1	1	yes	characteristic, complemented
12	C₃×C₉	D₄	1	1	yes	characteristic, complemented, Sylow
13	C₃×D₄	—	3	1	no	—
14	D₁₂	C₉	1	1	yes	characteristic, direct product factor
15	C₂×C₃²	C₂²×C₃	1	1	yes	characteristic
16	C₃×D₃	—	2	2	no	—
17	C₂×C₉	—	2	1	no	—
18	C₂×C₉	—	6	2	no	—
19	C₂×C₉	C₂×D₃	1	1	yes	characteristic
20	C₂²×C₃	—	3	2	no	—
21	C₂×D₃	C₂×C₉	1	2	yes	complemented
22	C₃×C₄	—	2	1	no	—
23	C₃×C₄	C₂×C₉	1	1	yes	characteristic, complemented
24	C₃×C₄	C₃×D₃	1	1	yes	characteristic
25	C₃²	C₃×D₄	1	1	yes	characteristic
26	C₉	—	2	1	no	—
27	C₉	D₁₂	1	1	yes	characteristic, direct product factor
28	D₄	—	3	1	no	Sylow
29	C₂×C₃	—	2	1	no	—
30	C₂×C₃	—	6	2	no	—
31	C₂×C₃	C₂²×C₉	1	1	yes	characteristic
32	C₂×C₃	C₂×C₃×D₃	1	1	yes	characteristic
33	D₃	—	2	2	no	—
34	C₂²	—	3	2	no	—
35	C₄	D₃×C₉	1	1	yes	characteristic, complemented
36	C₃	—	2	1	no	—
37	C₃	D₄×C₉	1	1	yes	characteristic, complemented
38	C₃	C₃×D₁₂	1	1	yes	characteristic
39	C₂	—	6	2	no	—
40	C₂	C₂×D₃×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.