Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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. #19128499 | C2 | semidirect |
| 2. C2×#14581820 | C2 | semidirect |
| 3. C2×#14581817 | C2 | semidirect |
| 4. #19127971 | C2 | semidirect |
| 5. #19127964 | C2 | semidirect |
| 6. #19127750 | C2 | semidirect |
| 7. #19127683 | C2 | semidirect |
| 8. C2×#14581708 | C2 | semidirect |
| 9. #568×C83 | C2 | semidirect |
| 13. #14581822 | C22 | semidirect |
| 19. #14581817 | C22 | semidirect |
| 21. C2×#13050579 | C22 | semidirect |
| 23. C2×D664 | C22 | semidirect |
| 27. #14581728 | C22 | semidirect |
| 28. #14581710 | C22 | semidirect |
| 29. #14581708 | C22 | semidirect |
| 30. #14581708 | C22 | semidirect |
| 33. #131×C83 | C22 | semidirect |
| 148. C83 | #3068 | semidirect |
| 152. #568 | D83 | semidirect |
| 175. #131 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128499 | 2 |
| C2×#14581820 | 2 |
| C2×#14581817 | 2 |
| #19127971 | 2 |
| #19127964 | 2 |
| #19127750 | 2 |
| #19127683 | 2 |
| C2×#14581708 | 2 |
| #568×C83 | 2 |
| #3068 | 83 |