Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19128332 | C2 | semidirect |
| 3. #19128064 | C2 | semidirect |
| 4. #19128059 | C2 | semidirect |
| 5. #19128054 | C2 | semidirect |
| 6. #19128046 | C2 | semidirect |
| 7. #19127706 | C2 | semidirect |
| 8. #19127700 | C2 | semidirect |
| 9. #19127698 | C2 | semidirect |
| 10. #19127656 | C2 | semidirect |
| 11. C2×#102×C83 | C2 | semidirect |
| 15. #14581791 | C22 | semidirect |
| 18. #14581783 | C22 | semidirect |
| 26. #14581717 | C22 | semidirect |
| 27. #14581717 | C22 | semidirect |
| 28. #14581715 | C22 | semidirect |
| 29. #14581714 | C22 | semidirect |
| 30. #14581714 | C22 | semidirect |
| 33. #14581712 | C22 | semidirect |
| 34. #14581702 | C22 | semidirect |
| 35. C8×Dic83 | C22 | semidirect |
| 136. C83 | #3136 | semidirect |
| 146. C2×#102 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128332 | 2 |
| #19128268 | 2 |
| #19128064 | 2 |
| #19128059 | 2 |
| #19128054 | 2 |
| #19128046 | 2 |
| #19127706 | 2 |
| #19127700 | 2 |
| #19127698 | 2 |
| #19127656 | 2 |
| C2×#102×C83 | 2 |
| #3136 | 83 |