Subgroups — C₂×C₄×Dic₃ #922

Order 96.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₃	C₂	1	2	yes	maximal
3	C₄×Dic₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄²	—	3	1	no	maximal, Sylow
5	C₂³×C₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄	C₄	1	4	yes	complemented
7	C₂×C₃×C₄	C₂²	1	2	yes	—
8	C₂×Dic₃	C₄	1	8	yes	direct product factor
9	C₂×Dic₃	C₂²	1	4	yes	—
10	C₂²×C₄	—	3	2	no	—
11	C₂²×C₄	D₃	1	1	yes	characteristic
12	C₄²	—	3	4	no	—
13	C₂²×C₃	C₂×C₄	1	4	yes	—
14	C₂²×C₃	C₂×C₄	1	2	yes	—
15	C₂²×C₃	C₂³	1	1	yes	characteristic
16	C₃×C₄	C₂×C₄	1	4	yes	complemented
17	Dic₃	C₂×C₄	1	8	yes	direct product factor
18	C₂³	C₂×D₃	1	1	yes	characteristic
19	C₂×C₄	—	3	8	no	—
20	C₂×C₄	—	3	4	no	—
21	C₂×C₄	Dic₃	1	4	yes	direct product factor
22	C₂×C₄	C₂×D₃	1	2	yes	—
23	C₂×C₃	C₄²	1	4	yes	complemented
24	C₂×C₃	C₂²×C₄	1	2	yes	—
25	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
26	C₂²	C₄×D₃	1	4	yes	—
27	C₂²	C₂×Dic₃	1	2	yes	—
28	C₂²	C₂²×D₃	1	1	yes	characteristic
29	C₄	—	3	8	no	—
30	C₄	C₂×Dic₃	1	4	yes	direct product factor
31	C₃	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
32	C₂	C₄×Dic₃	1	4	yes	direct product factor
33	C₂	C₂×C₄×D₃	1	2	yes	—
34	C₂	C₂²×Dic₃	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.