Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #19128041 | C2 | semidirect |
| 4. #19127997 | C2 | semidirect |
| 5. #19127991 | C2 | semidirect |
| 6. #19127908 | C2 | semidirect |
| 8. #19127805 | C2 | semidirect |
| 9. #19127802 | C2 | semidirect |
| 10. #19127757 | C2 | semidirect |
| 11. #461×C83 | C2 | semidirect |
| 137. C83 | #3116 | semidirect |
| 144. #461 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128256 | 2 |
| C4×#13050589 | 2 |
| #19128041 | 2 |
| #19127997 | 2 |
| #19127991 | 2 |
| #19127908 | 2 |
| #19127860 | 2 |
| #19127805 | 2 |
| #19127802 | 2 |
| #19127757 | 2 |
| #461×C83 | 2 |
| #3116 | 83 |