Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 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. #19128233 | C2 | semidirect |
| 3. #19128082 | C2 | semidirect |
| 4. #19128057 | C2 | semidirect |
| 5. #19127908 | C2 | semidirect |
| 6. #19127902 | C2 | semidirect |
| 7. #19127896 | C2 | semidirect |
| 8. #19127866 | C2 | semidirect |
| 9. #19127845 | C2 | semidirect |
| 10. #19127753 | C2 | semidirect |
| 11. #461×C83 | C2 | semidirect |
| 145. C83 | #3212 | semidirect |
| 151. #461 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128252 | 2 |
| #19128233 | 2 |
| #19128082 | 2 |
| #19128057 | 2 |
| #19127908 | 2 |
| #19127902 | 2 |
| #19127896 | 2 |
| #19127866 | 2 |
| #19127845 | 2 |
| #19127753 | 2 |
| #461×C83 | 2 |
| #3212 | 83 |