Subgroups — C₃×D₁₂ #631

Order 72.

35 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃	C₂	1	2	yes	maximal, complemented
2	C₃²×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₄	—	3	1	no	maximal
4	D₁₂	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₃²	C₂²	1	1	yes	characteristic
6	C₃×D₃	—	2	2	no	—
7	C₂²×C₃	—	3	2	no	—
8	C₂×D₃	C₂×C₃	1	2	yes	complemented
9	C₃×C₄	—	2	1	no	—
10	C₃×C₄	D₃	1	1	yes	characteristic, complemented
11	C₃×C₄	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃²	D₄	1	1	yes	characteristic, complemented, Sylow
13	D₄	—	3	1	no	Sylow
14	C₂×C₃	—	2	1	no	—
15	C₂×C₃	—	6	2	no	—
16	C₂×C₃	C₂×D₃	1	1	yes	characteristic
17	C₂×C₃	C₂²×C₃	1	1	yes	characteristic
18	D₃	—	2	2	no	—
19	C₂²	—	3	2	no	—
20	C₄	C₃×D₃	1	1	yes	characteristic, complemented
21	C₃	—	2	1	no	—
22	C₃	D₁₂	1	1	yes	characteristic, direct product factor
23	C₃	C₃×D₄	1	1	yes	characteristic, complemented
24	C₂	—	6	2	no	—
25	C₂	C₂×C₃×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.