Subgroups — C₃×D₄ #69

Order 24.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃	C₂	1	2	yes	maximal, complemented
2	C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃	—	2	2	no	—
5	C₂×C₃	C₂²	1	1	yes	characteristic
6	C₂²	C₂×C₃	1	2	yes	complemented
7	C₄	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃	D₄	1	1	yes	characteristic, direct product factor, Sylow
9	C₂	—	2	2	no	—
10	C₂	C₂²×C₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	C₂²
commutator, Frattini, cosocle	C₂	C₂²×C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ G

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.