Subgroups — C₁₁₃×C₇₃⋊C₃ #37613232

Order 24747.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×C₁₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₁₃	—	73	1	no	maximal, Hall
3	C₇₃⋊C₃	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₁₃	C₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
5	C₇₃	C₃×C₁₁₃	1	1	yes	characteristic, complemented, Sylow
6	C₃	—	73	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁₃	C₇₃⋊C₃
commutator, cosocle, hypocenter	C₇₃	C₃×C₁₁₃
Frattini	C₁	G
Fitting, socle	C₇₃×C₁₁₃	C₃
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₁₁₃

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.