Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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. #16863927 | C2 | semidirect |
| 2. C2×D4×Dic67 | C2 | semidirect |
| 3. #16863727 | C2 | semidirect |
| 4. #16863707 | C2 | semidirect |
| 5. #16863698 | C2 | semidirect |
| 6. #16863609 | C2 | semidirect |
| 7. #16863547 | C2 | semidirect |
| 8. #16863508 | C2 | semidirect |
| 9. #16863493 | C2 | semidirect |
| 10. #16863450 | C2 | semidirect |
| 15. #14524034 | C22 | semidirect |
| 16. #14524030 | C22 | semidirect |
| 19. #14524008 | C22 | semidirect |
| 25. D4×Dic67 | C22 | semidirect |
| 30. #14523976 | C22 | semidirect |
| 31. #14523975 | C22 | semidirect |
| 32. Dic67⋊C8 | C22 | semidirect |
| 33. #14523968 | C22 | semidirect |
| 35. #14523964 | C22 | semidirect |
| 37. #14523953 | C22 | semidirect |
| 141. C67 | #3114 | semidirect |