Subgroups — D₇₂₃₂ #28388787

Order 14464.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₆₁₆	C₂	1	2	yes	maximal, complemented
2	C₆₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₈₀₈	—	2	2	no	—
4	C₃₂×C₁₁₃	C₂²	1	1	yes	characteristic
5	D₉₀₄	—	4	2	no	—
6	C₁₆×C₁₁₃	D₄	1	1	yes	characteristic
7	D₄₅₂	—	8	2	no	—
8	C₈×C₁₁₃	D₈	1	1	yes	characteristic
9	C₂×D₁₁₃	—	16	2	no	—
10	C₄×C₁₁₃	D₁₆	1	1	yes	characteristic
11	C₂×C₁₁₃	D₃₂	1	1	yes	characteristic
12	D₁₁₃	—	32	2	no	—
13	D₆₄	—	113	1	no	maximal, Sylow
14	C₁₁₃	D₆₄	1	1	yes	characteristic, complemented, Sylow
15	D₃₂	—	113	2	no	—
16	C₆₄	D₁₁₃	1	1	yes	characteristic, complemented
17	D₁₆	—	226	2	no	—
18	C₃₂	C₂×D₁₁₃	1	1	yes	characteristic
19	D₈	—	452	2	no	—
20	C₁₆	D₄₅₂	1	1	yes	characteristic
21	D₄	—	904	2	no	—
22	C₈	D₉₀₄	1	1	yes	characteristic
23	C₂²	—	1808	2	no	—
24	C₄	D₁₈₀₈	1	1	yes	characteristic
25	C₂	—	3616	2	no	—
26	C₂	D₃₆₁₆	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.