Subgroups — C₆₇×D₁₆₇ #36375447

Order 22378.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₆₇	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₆₇	C₂×C₆₇	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₆₇	—	167	1	no	maximal, Hall
5	C₆₇	D₁₆₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	167	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₆₇	D₁₆₇
commutator, cosocle, hypocenter	C₁₆₇	C₂×C₆₇
Frattini	C₁	G
Fitting, socle	C₆₇×C₁₆₇	C₂
LCS	G ▷ C₁₆₇
UCS	C₁ ◁ C₆₇

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.