Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 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. #16863932 | C2 | semidirect |
| 2. C2×#14524030 | C2 | semidirect |
| 3. #16863777 | C2 | semidirect |
| 4. #16863749 | C2 | semidirect |
| 5. #16863616 | C2 | semidirect |
| 6. #16863610 | C2 | semidirect |
| 7. #16863551 | C2 | semidirect |
| 8. #16863537 | C2 | semidirect |
| 10. #16863446 | C2 | semidirect |
| 11. #450×C67 | C2 | semidirect |
| 13. C2×#11761618 | C22 | semidirect |
| 14. C2×#11761617 | C22 | semidirect |
| 17. #14524034 | C22 | semidirect |
| 18. #14524032 | C22 | semidirect |
| 25. Q8×Dic67 | C22 | semidirect |
| 26. #14524005 | C22 | semidirect |
| 32. Dic67⋊C8 | C22 | semidirect |
| 33. #14523968 | C22 | semidirect |
| 34. #14523966 | C22 | semidirect |
| 37. C8×Dic67 | C22 | semidirect |
| 144. C67 | #3211 | semidirect |
| 152. #450 | D67 | semidirect |