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. C4×#14579699 | C2 | semidirect |
| 2. #23781986 | C2 | semidirect |
| 3. #23781947 | C2 | semidirect |
| 4. #23781942 | C2 | semidirect |
| 5. #23781862 | C2 | semidirect |
| 6. #23781857 | C2 | semidirect |
| 7. #23781808 | C2 | semidirect |
| 8. #23781775 | C2 | semidirect |
| 9. #23781765 | C2 | semidirect |
| 10. #23781722 | C2 | semidirect |
| 11. #532×C163 | C2 | semidirect |
| 85. Dic326 | #41 | semidirect |
| 87. D652 | #41 | semidirect |
| 144. C163 | #3115 | semidirect |
| 146. #532 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579699 | 2 |
| #23781986 | 2 |
| #23781947 | 2 |
| #23781942 | 2 |
| #23781862 | 2 |
| #23781857 | 2 |
| #23781808 | 2 |
| #23781775 | 2 |
| #23781765 | 2 |
| #23781722 | 2 |
| #532×C163 | 2 |
| #3115 | 163 |