Subgroups — C₂×C₃×Dic₃ #632

Order 72.

37 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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