Subgroups — D₁₆₆₇⋊C₇ #37552307

Order 23338.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₆₆₇⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₆₆₇	C₇	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₆₆₇	C₂×C₇	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₇	—	1667	1	no	maximal, Hall
5	C₇	—	1667	1	no	Sylow
6	C₂	—	11669	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₆₆₇	C₂×C₇
LCS	G ▷ C₁₆₆₇
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.