Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782401 | C2 | semidirect |
| 2. #23782335 | C2 | semidirect |
| 3. #23782053 | C2 | semidirect |
| 4. #23781878 | C2 | semidirect |
| 5. #23781862 | C2 | semidirect |
| 6. #23781858 | C2 | semidirect |
| 7. #23781857 | C2 | semidirect |
| 8. #23781795 | C2 | semidirect |
| 9. #23781777 | C2 | semidirect |
| 10. C4×#14579688 | C2 | semidirect |
| 11. #493×C163 | C2 | semidirect |
| 108. C8×C163 | #41 | semidirect |
| 134. C163 | #3399 | semidirect |
| 139. #493 | D163 | semidirect |
| 243. C8 | #14579698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782401 | 2 |
| #23782335 | 2 |
| #23782053 | 2 |
| #23781878 | 2 |
| #23781862 | 2 |
| #23781858 | 2 |
| #23781857 | 2 |
| #23781795 | 2 |
| #23781777 | 2 |
| C4×#14579688 | 2 |
| #493×C163 | 2 |
| #3399 | 163 |