Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
406 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19128425 | C2 | semidirect |
| 2. #19128371 | C2 | semidirect |
| 3. #19128087 | C2 | semidirect |
| 4. #19127918 | C2 | semidirect |
| 5. #19127903 | C2 | semidirect |
| 6. #19127899 | C2 | semidirect |
| 7. #19127893 | C2 | semidirect |
| 8. #19127831 | C2 | semidirect |
| 9. #19127802 | C2 | semidirect |
| 10. C4×D664 | C2 | semidirect |
| 11. #492×C83 | C2 | semidirect |
| 105. C8×C83 | #41 | semidirect |
| 133. C83 | #3397 | semidirect |
| 137. #492 | D83 | semidirect |
| 239. C8 | #13050589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128425 | 2 |
| #19128371 | 2 |
| #19128087 | 2 |
| #19127918 | 2 |
| #19127903 | 2 |
| #19127899 | 2 |
| #19127893 | 2 |
| #19127831 | 2 |
| #19127802 | 2 |
| C4×D664 | 2 |
| #492×C83 | 2 |
| #3397 | 83 |