Subgroups — C₁₇⋊D₁₇ #10596804

Order 578.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇²	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₁₇	—	17	18	no	maximal
3	C₁₇	D₁₇	1	18	yes	complemented
4	C₂	—	289	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇²	C₂
LCS	G ▷ C₁₇²
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₇²	C₂	semidirect
3. C₁₇	D₁₇	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₇²	2
D₁₇	17