Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #19127657 | C2 | semidirect |
| 5. C2×#14581703 | C2 | semidirect |
| 6. #19127465 | C2 | semidirect |
| 7. #339×C83 | C2 | semidirect |
| 10. #14581800 | C4 | semidirect |
| 16. #14581720 | C4 | semidirect |
| 17. #14581715 | C4 | semidirect |
| 18. #14581712 | C4 | semidirect |
| 99. C83 | #1765 | semidirect |
| 106. #339 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581800 | 2 |
| C2×#14581720 | 2 |
| #19127695 | 2 |
| #19127657 | 2 |
| C2×#14581703 | 2 |
| #19127465 | 2 |
| #339×C83 | 2 |
| #1765 | 83 |