Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
444 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 444 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. #16863948 | C2 | semidirect |
| 3. #16863731 | C2 | semidirect |
| 4. #16863675 | C2 | semidirect |
| 5. #16863600 | C2 | semidirect |
| 8. #16863499 | C2 | semidirect |
| 9. #16863495 | C2 | semidirect |
| 10. #16863450 | C2 | semidirect |
| 11. #484×C67 | C2 | semidirect |
| 16. #14524042 | C22 | semidirect |
| 17. #14524041 | C22 | semidirect |
| 21. Q8×Dic67 | C22 | semidirect |
| 23. #14524008 | C22 | semidirect |
| 31. #14523976 | C22 | semidirect |
| 32. Dic67⋊C8 | C22 | semidirect |
| 33. #14523966 | C22 | semidirect |
| 37. #14523953 | C22 | semidirect |
| 40. #107×C67 | C22 | semidirect |
| 41. #103×C67 | C22 | semidirect |
| 137. C67 | #3110 | semidirect |
| 141. #484 | D67 | semidirect |
| 171. #107 | C2×D67 | semidirect |
| 174. #103 | C2×D67 | semidirect |