Subgroups — #63231

Order 272.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₇	C₂	1	1	yes	maximal, characteristic
2	Dic₃₄	C₂	1	1	yes	maximal, characteristic
3	#3622	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₇	—	2	1	no	—
5	C₄×C₁₇	C₂²	1	1	yes	characteristic
6	Dic₁₇	—	2	1	no	—
7	C₂×C₁₇	D₄	1	1	yes	characteristic
8	C₁₇	Q₁₆	1	1	yes	characteristic, complemented, Sylow
9	Q₁₆	—	17	1	no	maximal, Sylow
10	Q₈	—	17	1	no	—
11	Q₈	D₁₇	1	1	yes	characteristic
12	C₈	—	17	1	no	—
13	C₄	—	2	1	no	—
14	C₄	—	34	1	no	—
15	C₄	C₂×D₁₇	1	1	yes	characteristic
16	C₂	C₂²⋊D₁₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. C₁₇	Q₁₆	semidirect

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