Subgroups — D₅₆ #1133

Order 112.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₈	C₂	1	2	yes	maximal, complemented
2	C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₇	—	2	2	no	—
4	C₄×C₇	C₂²	1	1	yes	characteristic
5	D₈	—	7	1	no	maximal, Sylow
6	C₂×C₇	D₄	1	1	yes	characteristic
7	D₇	—	4	2	no	—
8	D₄	—	7	2	no	—
9	C₈	D₇	1	1	yes	characteristic, complemented
10	C₇	D₈	1	1	yes	characteristic, complemented, Sylow
11	C₂²	—	14	2	no	—
12	C₄	C₂×D₇	1	1	yes	characteristic
13	C₂	—	28	2	no	—
14	C₂	D₂₈	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.