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. #19128249 | C2 | semidirect |
| 2. #19128233 | C2 | semidirect |
| 3. #19128003 | C2 | semidirect |
| 4. #19127987 | C2 | semidirect |
| 5. #19127981 | C2 | semidirect |
| 6. #19127951 | C2 | semidirect |
| 7. #19127946 | C2 | semidirect |
| 8. #19127914 | C2 | semidirect |
| 9. #19127898 | C2 | semidirect |
| 10. #19127723 | C2 | semidirect |
| 11. #459×C83 | C2 | semidirect |
| 142. C83 | #3251 | semidirect |
| 152. #459 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128249 | 2 |
| #19128233 | 2 |
| #19128003 | 2 |
| #19127987 | 2 |
| #19127981 | 2 |
| #19127951 | 2 |
| #19127946 | 2 |
| #19127914 | 2 |
| #19127898 | 2 |
| #19127723 | 2 |
| #459×C83 | 2 |
| #3251 | 83 |