Subgroups — C₂×D₆₈ #63251

Order 272.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₇	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₆₈	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₇	C₂²	1	1	yes	characteristic
5	C₂×D₁₇	—	2	4	no	—
6	C₂×D₁₇	C₂²	1	4	yes	complemented
7	C₄×C₁₇	C₂²	1	2	yes	complemented
8	C₂×C₁₇	D₄	1	2	yes	complemented
9	C₂×C₁₇	C₂³	1	1	yes	characteristic
10	D₁₇	—	2	4	no	—
11	C₁₇	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
12	C₂×D₄	—	17	1	no	maximal, Sylow
13	C₂³	—	17	2	no	—
14	D₄	—	17	4	no	—
15	C₂×C₄	D₁₇	1	1	yes	characteristic, complemented
16	C₂²	—	17	4	no	—
17	C₂²	—	34	4	no	—
18	C₂²	C₂×D₁₇	1	1	yes	characteristic
19	C₄	C₂×D₁₇	1	2	yes	complemented
20	C₂	—	34	4	no	—
21	C₂	D₆₈	1	2	yes	direct product factor
22	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.