Subgroups — C₂³×Dic₃ #1011

Order 96.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₃	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₄	—	3	1	no	maximal, Sylow
4	C₂³×C₃	C₄	1	8	yes	complemented
5	C₂³×C₃	C₂²	1	7	yes	—
6	C₂×Dic₃	C₂²	1	28	yes	direct product factor
7	C₂⁴	D₃	1	1	yes	characteristic
8	C₂²×C₄	—	3	14	no	—
9	C₂²×C₃	C₂×C₄	1	28	yes	complemented
10	C₂²×C₃	C₂³	1	7	yes	—
11	Dic₃	C₂³	1	8	yes	direct product factor
12	C₂³	Dic₃	1	8	yes	direct product factor
13	C₂³	C₂×D₃	1	7	yes	—
14	C₂×C₄	—	3	28	no	—
15	C₂×C₃	C₂²×C₄	1	14	yes	complemented
16	C₂×C₃	C₂⁴	1	1	yes	characteristic
17	C₂²	C₂×Dic₃	1	28	yes	direct product factor
18	C₂²	C₂²×D₃	1	7	yes	—
19	C₄	—	3	8	no	—
20	C₃	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
21	C₂	C₂²×Dic₃	1	14	yes	direct product factor
22	C₂	C₂³×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.