Subgroups — C₃⋊D₂₁ #1266

Order 126.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₁	—	3	4	no	maximal
3	C₃×C₇	D₃	1	4	yes	complemented
4	C₃⋊D₃	—	7	1	no	maximal, Hall
5	D₇	—	9	1	no	Hall
6	C₃²	D₇	1	1	yes	characteristic, complemented, Sylow
7	C₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
8	D₃	—	21	4	no	—
9	C₃	D₂₁	1	4	yes	complemented
10	C₂	—	63	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁

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.