Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782215 | C2 | semidirect |
| 2. C4×#14579699 | C2 | semidirect |
| 3. #23781990 | C2 | semidirect |
| 4. #23781951 | C2 | semidirect |
| 5. #23781946 | C2 | semidirect |
| 6. #23781866 | C2 | semidirect |
| 7. #23781861 | C2 | semidirect |
| 8. #23781812 | C2 | semidirect |
| 9. #23781778 | C2 | semidirect |
| 10. #23781767 | C2 | semidirect |
| 11. #432×C163 | C2 | semidirect |
| 87. Dic326 | #41 | semidirect |
| 93. D652 | #41 | semidirect |
| 144. C163 | #3115 | semidirect |
| 156. #432 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782215 | 2 |
| C4×#14579699 | 2 |
| #23781990 | 2 |
| #23781951 | 2 |
| #23781946 | 2 |
| #23781866 | 2 |
| #23781861 | 2 |
| #23781812 | 2 |
| #23781778 | 2 |
| #23781767 | 2 |
| #432×C163 | 2 |
| #3115 | 163 |