Subgroups — C₃×C₁₇₂₃⋊C₃ #29509302

Order 15507.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇₂₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₁₇₂₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₁₇₂₃	C₃²	1	1	yes	characteristic, complemented, Sylow
4	C₃²	—	1723	1	no	maximal, Sylow
5	C₃	—	1723	3	no	—
6	C₃	C₁₇₂₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃	C₁₇₂₃⋊C₃
commutator, cosocle, hypocenter	C₁₇₂₃	C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₇₂₃	C₃
LCS	G ▷ C₁₇₂₃
UCS	C₁ ◁ C₃

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.