Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
366 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 366 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. #19128256 | C2 | semidirect |
| 3. #19128109 | C2 | semidirect |
| 4. #19128064 | C2 | semidirect |
| 5. #19128028 | C2 | semidirect |
| 6. #19128024 | C2 | semidirect |
| 7. #19127992 | C2 | semidirect |
| 8. #19127991 | C2 | semidirect |
| 9. #19127978 | C2 | semidirect |
| 10. #19127757 | C2 | semidirect |
| 11. #474×C83 | C2 | semidirect |
| 139. C83 | #3235 | semidirect |
| 149. #474 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128256 | 2 |
| #19128248 | 2 |
| #19128109 | 2 |
| #19128064 | 2 |
| #19128028 | 2 |
| #19128024 | 2 |
| #19127992 | 2 |
| #19127991 | 2 |
| #19127978 | 2 |
| #19127757 | 2 |
| #474×C83 | 2 |
| #3235 | 83 |