Subgroups — D₃×C₅₅₆₉ #45689152

Order 33414.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₅₆₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₅₅₆₉	—	3	1	no	maximal, Hall
3	C₅₅₆₉	D₃	1	1	yes	characteristic, direct product factor, Sylow
4	D₃	C₅₅₆₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃	C₂×C₅₅₆₉	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₅₆₉	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₅₅₆₉
Frattini	C₁	G
Fitting, socle	C₃×C₅₅₆₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₅₅₆₉

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.