Subgroups — C₁₇₃×C₆₇⋊C₃ #46851971

Order 34773.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×C₁₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₇₃	—	67	1	no	maximal, Hall
3	C₆₇⋊C₃	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₇₃	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
5	C₆₇	C₃×C₁₇₃	1	1	yes	characteristic, complemented, Sylow
6	C₃	—	67	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇₃	C₆₇⋊C₃
commutator, cosocle, hypocenter	C₆₇	C₃×C₁₇₃
Frattini	C₁	G
Fitting, socle	C₆₇×C₁₇₃	C₃
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₁₇₃

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.