Subgroups — #34086471

Order 19568.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₈₉₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₂₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₁₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₂₂₃	—	2	1	no	—
5	C₂×D₁₂₂₃	—	2	1	no	—
6	C₄×C₁₂₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₁₂₂₃	—	4	1	no	—
8	C₂×C₁₂₂₃	D₄	1	1	yes	characteristic
9	D₁₂₂₃	—	4	1	no	—
10	C₁₂₂₃	D₈	1	1	yes	characteristic, complemented, Sylow
11	D₈	—	1223	1	no	maximal, Sylow
12	D₄	—	1223	1	no	—
13	D₄	D₁₂₂₃	1	1	yes	characteristic, complemented
14	C₈	—	1223	1	no	—
15	C₂²	—	2	1	no	—
16	C₂²	—	2446	1	no	—
17	C₄	C₂×D₁₂₂₃	1	1	yes	characteristic
18	C₂	—	4	1	no	—
19	C₂	—	4892	1	no	—
20	C₂	C₂²⋊D₁₂₂₃	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.