Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#14581817 | C2 | semidirect |
| 2. C22×D664 | C2 | semidirect |
| 3. #19128265 | C2 | semidirect |
| 4. #19128175 | C2 | semidirect |
| 5. #19127919 | C2 | semidirect |
| 6. #19127895 | C2 | semidirect |
| 7. #19127727 | C2 | semidirect |
| 8. #19127705 | C2 | semidirect |
| 9. #416×C83 | C2 | semidirect |
| 13. C2×#13050577 | C22 | semidirect |
| 16. C2×#13050575 | C22 | semidirect |
| 18. #14581788 | C22 | semidirect |
| 19. #14581781 | C22 | semidirect |
| 23. #14581754 | C22 | semidirect |
| 26. Dic83⋊C8 | C22 | semidirect |
| 27. #14581712 | C22 | semidirect |
| 31. #103×C83 | C22 | semidirect |
| 32. #102×C83 | C22 | semidirect |
| 40. C2×D332 | D4 | semidirect |
| 122. C83 | #3041 | semidirect |
| 131. #416 | D83 | semidirect |
| 152. #103 | C2×D83 | semidirect |
| 154. #102 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581817 | 2 |
| C22×D664 | 2 |
| #19128265 | 2 |
| #19128175 | 2 |
| #19127919 | 2 |
| #19127895 | 2 |
| #19127727 | 2 |
| #19127705 | 2 |
| #416×C83 | 2 |
| #3041 | 83 |