Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
392 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 392 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. #19128004 | C2 | semidirect |
| 4. #19127983 | C2 | semidirect |
| 5. #19127953 | C2 | semidirect |
| 6. #19127948 | C2 | semidirect |
| 7. #19127915 | C2 | semidirect |
| 8. #19127902 | C2 | semidirect |
| 9. #19127896 | C2 | semidirect |
| 10. #19127723 | C2 | semidirect |
| 11. #474×C83 | C2 | semidirect |
| 142. C83 | #3251 | semidirect |
| 147. #474 | 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 |
| #19128004 | 2 |
| #19127983 | 2 |
| #19127953 | 2 |
| #19127948 | 2 |
| #19127915 | 2 |
| #19127902 | 2 |
| #19127896 | 2 |
| #19127723 | 2 |
| #474×C83 | 2 |
| #3251 | 83 |