Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
454 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 454 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. #16863927 | C2 | semidirect |
| 2. C2×#14524005 | C2 | semidirect |
| 3. #16863731 | C2 | semidirect |
| 4. #16863695 | C2 | semidirect |
| 5. #16863610 | C2 | semidirect |
| 6. #16863549 | C2 | semidirect |
| 8. #16863483 | C2 | semidirect |
| 9. #16863476 | C2 | semidirect |
| 10. #16863446 | C2 | semidirect |
| 11. #481×C67 | C2 | semidirect |
| 17. #14524034 | C22 | semidirect |
| 18. #14524030 | C22 | semidirect |
| 21. #14524008 | C22 | semidirect |
| 23. D4×Dic67 | C22 | semidirect |
| 31. #14523976 | C22 | semidirect |
| 32. Dic67⋊C8 | C22 | semidirect |
| 33. #14523966 | C22 | semidirect |
| 37. C8×Dic67 | C22 | semidirect |
| 40. #106×C67 | C22 | semidirect |
| 41. #102×C67 | C22 | semidirect |
| 141. C67 | #3105 | semidirect |
| 145. #481 | D67 | semidirect |
| 175. #106 | C2×D67 | semidirect |
| 180. #102 | C2×D67 | semidirect |