Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782385 | C2 | semidirect |
| 3. #23782012 | C2 | semidirect |
| 4. #23781990 | C2 | semidirect |
| 5. #23781951 | C2 | semidirect |
| 6. #23781894 | C2 | semidirect |
| 7. #23781866 | C2 | semidirect |
| 8. #23781829 | C2 | semidirect |
| 9. C4×Dic652 | C2 | semidirect |
| 10. #23781662 | C2 | semidirect |
| 11. C8×D4×C163 | C2 | semidirect |
| 127. C163 | #3304 | semidirect |
| 138. C8×D4 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782385 | 2 |
| #23782336 | 2 |
| #23782012 | 2 |
| #23781990 | 2 |
| #23781951 | 2 |
| #23781894 | 2 |
| #23781866 | 2 |
| #23781829 | 2 |
| C4×Dic652 | 2 |
| #23781662 | 2 |
| C8×D4×C163 | 2 |
| #3304 | 163 |