Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19128251 | C2 | semidirect |
| 2. #19128235 | C2 | semidirect |
| 3. #19128002 | C2 | semidirect |
| 4. #19127987 | C2 | semidirect |
| 5. #19127982 | C2 | semidirect |
| 6. #19127954 | C2 | semidirect |
| 7. #19127947 | C2 | semidirect |
| 8. #19127917 | C2 | semidirect |
| 9. #19127902 | C2 | semidirect |
| 10. #19127897 | C2 | semidirect |
| 11. #423×C83 | C2 | semidirect |
| 142. C83 | #3251 | semidirect |
| 153. #423 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128251 | 2 |
| #19128235 | 2 |
| #19128002 | 2 |
| #19127987 | 2 |
| #19127982 | 2 |
| #19127954 | 2 |
| #19127947 | 2 |
| #19127917 | 2 |
| #19127902 | 2 |
| #19127897 | 2 |
| #423×C83 | 2 |
| #3251 | 83 |