Subgroups — #63229

Order 272.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₁₇	C₂	1	1	yes	maximal, characteristic
2	Dic₃₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#3622	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₇	—	2	1	no	—
5	C₄×C₁₇	C₂²	1	1	yes	characteristic
6	Dic₁₇	—	2	1	no	—
7	C₂×C₁₇	—	4	1	no	—
8	C₂×C₁₇	D₄	1	1	yes	characteristic
9	C₁₇	SD₁₆	1	1	yes	characteristic, complemented, Sylow
10	SD₁₆	—	17	1	no	maximal, Sylow
11	Q₈	—	17	1	no	—
12	D₄	D₁₇	1	1	yes	characteristic
13	C₈	—	17	1	no	—
14	C₂²	—	2	1	no	—
15	C₄	—	34	1	no	—
16	C₄	C₂×D₁₇	1	1	yes	characteristic
17	C₂	—	4	1	no	—
18	C₂	C₂²⋊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.