Subgroups — Dic₆₈ #63221

Order 272.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₄	C₂	1	2	yes	maximal
2	C₈×C₁₇	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₇	C₂²	1	1	yes	characteristic
4	Dic₁₇	—	2	2	no	—
5	C₂×C₁₇	D₄	1	1	yes	characteristic
6	C₁₇	Q₁₆	1	1	yes	characteristic, complemented, Sylow
7	Q₁₆	—	17	1	no	maximal, Sylow
8	Q₈	—	17	2	no	—
9	C₈	D₁₇	1	1	yes	characteristic
10	C₄	—	34	2	no	—
11	C₄	C₂×D₁₇	1	1	yes	characteristic
12	C₂	D₆₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. C₁₇	Q₁₆	semidirect

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