Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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. #16863767 | C2 | semidirect |
| 4. #16863741 | C2 | semidirect |
| 5. #16863595 | C2 | semidirect |
| 6. #16863594 | C2 | semidirect |
| 7. #16863549 | C2 | semidirect |
| 8. #16863547 | C2 | semidirect |
| 9. #16863546 | C2 | semidirect |
| 10. #16863446 | C2 | semidirect |
| 11. #450×C67 | C2 | semidirect |
| 15. C2×#11761617 | C22 | semidirect |
| 16. C2×#11761616 | C22 | semidirect |
| 17. C2×#11761615 | C22 | semidirect |
| 18. #14524042 | C22 | semidirect |
| 19. #14524041 | C22 | semidirect |
| 27. Q8×Dic67 | C22 | semidirect |
| 29. #14524008 | C22 | semidirect |
| 32. Dic67⋊C8 | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 34. #14523964 | C22 | semidirect |
| 35. #14523963 | C22 | semidirect |
| 37. C8×Dic67 | C22 | semidirect |
| 39. C2×SD16×C67 | C22 | semidirect |
| 41. #102×C67 | C22 | semidirect |
| 111. C2×Dic67 | SD16 | semidirect |
| 152. C67 | #3208 | semidirect |
| 162. #450 | D67 | semidirect |
| 171. C2×SD16 | C2×D67 | semidirect |
| 191. #102 | C2×D67 | semidirect |