Subgroups — D₆₈ #3627

Order 136.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₇	C₂	1	2	yes	maximal, complemented
2	C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇	C₂²	1	1	yes	characteristic
4	D₁₇	—	2	2	no	—
5	C₁₇	D₄	1	1	yes	characteristic, complemented, Sylow
6	D₄	—	17	1	no	maximal, Sylow
7	C₂²	—	17	2	no	—
8	C₄	D₁₇	1	1	yes	characteristic, complemented
9	C₂	—	34	2	no	—
10	C₂	C₂×D₁₇	1	1	yes	characteristic

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.