Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
434 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 113 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. #19128252 | C2 | semidirect |
| 2. #19128248 | C2 | semidirect |
| 3. #19128087 | C2 | semidirect |
| 4. #19128062 | C2 | semidirect |
| 5. #19127903 | C2 | semidirect |
| 6. #19127897 | C2 | semidirect |
| 7. #19127896 | C2 | semidirect |
| 8. #19127849 | C2 | semidirect |
| 9. #19127845 | C2 | semidirect |
| 10. #19127757 | C2 | semidirect |
| 11. #461×C83 | C2 | semidirect |
| 154. C83 | #3214 | semidirect |
| 160. #461 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128252 | 2 |
| #19128248 | 2 |
| #19128087 | 2 |
| #19128062 | 2 |
| #19127903 | 2 |
| #19127897 | 2 |
| #19127896 | 2 |
| #19127849 | 2 |
| #19127845 | 2 |
| #19127757 | 2 |
| #461×C83 | 2 |
| #3214 | 83 |