Subgroups — D₂₂₄ #89243

Order 448.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁₂	C₂	1	2	yes	maximal, complemented
2	C₇×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	D₅₆	—	2	2	no	—
4	C₇×C₁₆	C₂²	1	1	yes	characteristic
5	D₃₂	—	7	1	no	maximal, Sylow
6	D₂₈	—	4	2	no	—
7	C₇×C₈	D₄	1	1	yes	characteristic
8	D₁₆	—	7	2	no	—
9	C₃₂	D₇	1	1	yes	characteristic, complemented
10	C₂×D₇	—	8	2	no	—
11	C₄×C₇	D₈	1	1	yes	characteristic
12	D₈	—	14	2	no	—
13	C₁₆	C₂×D₇	1	1	yes	characteristic
14	C₂×C₇	D₁₆	1	1	yes	characteristic
15	D₇	—	16	2	no	—
16	D₄	—	28	2	no	—
17	C₈	D₂₈	1	1	yes	characteristic
18	C₇	D₃₂	1	1	yes	characteristic, complemented, Sylow
19	C₂²	—	56	2	no	—
20	C₄	D₅₆	1	1	yes	characteristic
21	C₂	—	112	2	no	—
22	C₂	D₁₁₂	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.