Subgroups — D₆₇₅₂ #27212982

Order 13504.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₃₇₆	C₂	1	2	yes	maximal, complemented
2	C₃₂×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆₈₈	—	2	2	no	—
4	C₁₆×C₂₁₁	C₂²	1	1	yes	characteristic
5	D₈₄₄	—	4	2	no	—
6	C₈×C₂₁₁	D₄	1	1	yes	characteristic
7	C₂×D₂₁₁	—	8	2	no	—
8	C₄×C₂₁₁	D₈	1	1	yes	characteristic
9	C₂×C₂₁₁	D₁₆	1	1	yes	characteristic
10	D₂₁₁	—	16	2	no	—
11	C₂₁₁	D₃₂	1	1	yes	characteristic, complemented, Sylow
12	D₃₂	—	211	1	no	maximal, Sylow
13	D₁₆	—	211	2	no	—
14	C₃₂	D₂₁₁	1	1	yes	characteristic, complemented
15	D₈	—	422	2	no	—
16	C₁₆	C₂×D₂₁₁	1	1	yes	characteristic
17	D₄	—	844	2	no	—
18	C₈	D₈₄₄	1	1	yes	characteristic
19	C₂²	—	1688	2	no	—
20	C₄	D₁₆₈₈	1	1	yes	characteristic
21	C₂	—	3376	2	no	—
22	C₂	D₃₃₇₆	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.