Subgroups — D₃×C₇₁ #88338

Order 426.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₇₁	—	3	1	no	maximal, Hall
3	C₇₁	D₃	1	1	yes	characteristic, direct product factor, Sylow
4	D₃	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃	C₂×C₇₁	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₁	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₇₁
Frattini	C₁	G
Fitting, socle	C₃×C₇₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₇₁

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.