Subgroups — #217

Order 48.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃	C₂	1	2	yes	maximal, complemented
3	C₂²⋊C₄	—	3	1	no	maximal, Sylow
4	C₂²×C₃	—	2	2	no	—
5	C₂²×C₃	C₄	1	2	yes	complemented
6	C₂²×C₃	C₂²	1	1	yes	characteristic
7	Dic₃	—	2	2	no	—
8	C₂³	D₃	1	1	yes	characteristic
9	C₂×C₄	—	3	2	no	—
10	C₂×C₃	—	2	2	no	—
11	C₂×C₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃	D₄	1	2	yes	—
13	C₂²	—	2	2	no	—
14	C₂²	Dic₃	1	2	yes	complemented
15	C₂²	C₂×D₃	1	1	yes	characteristic
16	C₄	—	6	2	no	—
17	C₃	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₂	—	2	2	no	—
19	C₂	C₂×Dic₃	1	1	yes	characteristic
20	C₂	#67	1	2	yes	—

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.