Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
238 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 59. C2×C4×C163 | Q16 | semidirect |
| 78. C163 | #1605 | semidirect |
| 137. C2×C4 | #14579689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781820 | 2 |
| #23781585 | 2 |
| #23781402 | 2 |
| #23781391 | 2 |
| #544×C163 | 2 |
| #1605 | 163 |