Subgroups — D₁₇×C₇₆₉ #39908482

Order 26146.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₇₆₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₇₆₉	—	17	1	no	maximal, Hall
3	C₇₆₉	D₁₇	1	1	yes	characteristic, direct product factor, Sylow
4	D₁₇	C₇₆₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₇	C₂×C₇₆₉	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₆₉	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₇₆₉
Frattini	C₁	G
Fitting, socle	C₁₇×C₇₆₉	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₇₆₉

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.