Subgroups — C₂²×Dic₆ #998

Order 96.

156 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	C₂×Dic₆	C₂	1	12	yes	maximal, direct product factor
4	C₂²×Q₈	—	3	1	no	maximal, Sylow
5	C₂³×C₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄	C₂²	1	6	yes	—
7	C₂×Dic₃	C₂²	1	12	yes	—
8	Dic₆	C₂²	1	16	yes	direct product factor
9	C₂×Q₈	—	3	12	no	—
10	C₂²×C₄	—	3	2	no	—
11	C₂²×C₄	D₃	1	1	yes	characteristic
12	C₂²×C₃	Q₈	1	4	yes	complemented
13	C₂²×C₃	C₂³	1	3	yes	—
14	C₃×C₄	C₂³	1	4	yes	—
15	Dic₃	C₂³	1	8	yes	—
16	C₂³	C₂×D₃	1	1	yes	characteristic
17	Q₈	—	3	16	no	—
18	C₂×C₄	—	3	12	no	—
19	C₂×C₄	C₂×D₃	1	6	yes	—
20	C₂×C₃	C₂×Q₈	1	6	yes	complemented
21	C₂×C₃	C₂⁴	1	1	yes	characteristic
22	C₂²	Dic₆	1	4	yes	direct product factor
23	C₂²	C₂²×D₃	1	3	yes	—
24	C₄	—	3	8	no	—
25	C₄	C₂²×D₃	1	4	yes	—
26	C₃	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
27	C₂	C₂×Dic₆	1	6	yes	direct product factor
28	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.