Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 1. #23781820 | C2 | semidirect |
| 3. #23781402 | C2 | semidirect |
| 53. C23×C163 | Q16 | semidirect |
| 87. C163 | #1602 | semidirect |
| 132. C23 | #14579689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781820 | 2 |
| #23781577 | 2 |
| #23781402 | 2 |
| #23781389 | 2 |
| #543×C163 | 2 |
| #1602 | 163 |