Subgroups — D₁₆₆₆₄ #45686751

Order 33328.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₃₃₂	C₂	1	2	yes	maximal, complemented
2	C₈×C₂₀₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₀₈₃	—	2	2	no	—
4	C₄×C₂₀₈₃	C₂²	1	1	yes	characteristic
5	C₂×C₂₀₈₃	D₄	1	1	yes	characteristic
6	D₂₀₈₃	—	4	2	no	—
7	C₂₀₈₃	D₈	1	1	yes	characteristic, complemented, Sylow
8	D₈	—	2083	1	no	maximal, Sylow
9	D₄	—	2083	2	no	—
10	C₈	D₂₀₈₃	1	1	yes	characteristic, complemented
11	C₂²	—	4166	2	no	—
12	C₄	C₂×D₂₀₈₃	1	1	yes	characteristic
13	C₂	—	8332	2	no	—
14	C₂	D₈₃₃₂	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.