Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
364 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 115 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. #16864110 | C2 | semidirect |
| 2. #16863800 | C2 | semidirect |
| 3. #16863719 | C2 | semidirect |
| 4. #16863717 | C2 | semidirect |
| 5. #16863684 | C2 | semidirect |
| 6. #16863629 | C2 | semidirect |
| 7. D8×Dic67 | C2 | semidirect |
| 8. C8×C22⋊D67 | C2 | semidirect |
| 9. #16863434 | C2 | semidirect |
| 10. #16863433 | C2 | semidirect |
| 11. #466×C67 | C2 | semidirect |
| 121. C67 | #3341 | semidirect |
| 128. #466 | D67 | semidirect |