Subgroups — C₃²×D₁₂ #6300

Order 216.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×D₃	C₂	1	2	yes	maximal, complemented
2	C₃³×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₄	—	3	1	no	maximal
4	C₃×D₁₂	C₃	1	4	yes	maximal, direct product factor
5	C₂×C₃³	C₂²	1	1	yes	characteristic
6	C₃²×D₃	—	2	2	no	—
7	C₂²×C₃²	—	3	2	no	—
8	C₂×C₃×D₃	C₂×C₃	1	8	yes	complemented
9	C₃²×C₄	—	2	4	no	—
10	C₃²×C₄	D₃	1	1	yes	characteristic, complemented
11	C₃²×C₄	C₂×C₃	1	4	yes	complemented
12	C₃³	D₄	1	1	yes	characteristic, complemented, Sylow
13	C₃×D₄	—	3	4	no	—
14	D₁₂	C₃²	1	1	yes	characteristic, direct product factor
15	C₂×C₃²	—	2	4	no	—
16	C₂×C₃²	—	6	2	no	—
17	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
18	C₂×C₃²	C₂²×C₃	1	4	yes	—
19	C₃×D₃	—	2	8	no	—
20	C₂²×C₃	—	3	8	no	—
21	C₂×D₃	C₂×C₃²	1	2	yes	complemented
22	C₃×C₄	—	2	4	no	—
23	C₃×C₄	C₃×D₃	1	4	yes	complemented
24	C₃×C₄	C₂×C₃²	1	1	yes	characteristic, complemented
25	C₃²	—	2	4	no	—
26	C₃²	D₁₂	1	1	yes	characteristic, direct product factor
27	C₃²	C₃×D₄	1	4	yes	complemented
28	D₄	—	3	1	no	Sylow
29	C₂×C₃	—	2	4	no	—
30	C₂×C₃	—	6	8	no	—
31	C₂×C₃	C₂×C₃×D₃	1	4	yes	—
32	C₂×C₃	C₂²×C₃²	1	1	yes	characteristic
33	D₃	—	2	2	no	—
34	C₂²	—	3	2	no	—
35	C₄	C₃²×D₃	1	1	yes	characteristic, complemented
36	C₃	—	2	4	no	—
37	C₃	C₃×D₁₂	1	4	yes	direct product factor
38	C₃	C₃²×D₄	1	1	yes	characteristic, complemented
39	C₂	—	6	2	no	—
40	C₂	C₂×C₃²×D₃	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.