Subgroups — C₃×C₂²⋊C₄ #219

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×C₃×C₄	C₂	1	2	yes	maximal, complemented
3	C₂²⋊C₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃	—	2	2	no	—
5	C₂²×C₃	C₄	1	2	yes	complemented
6	C₂²×C₃	C₂²	1	1	yes	characteristic
7	C₃×C₄	—	2	2	no	—
8	C₂³	C₂×C₃	1	1	yes	characteristic
9	C₂×C₄	C₂×C₃	1	2	yes	complemented
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	C₃×C₄	1	2	yes	complemented
15	C₂²	C₂²×C₃	1	1	yes	characteristic
16	C₄	—	2	2	no	—
17	C₃	C₂²⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
18	C₂	—	2	2	no	—
19	C₂	C₂×C₃×C₄	1	1	yes	characteristic
20	C₂	C₃×D₄	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.