Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
448 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 129 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. #16863727 | C2 | semidirect |
| 4. #16863724 | C2 | semidirect |
| 5. #16863684 | C2 | semidirect |
| 6. #16863599 | C2 | semidirect |
| 8. #16863487 | C2 | semidirect |
| 9. SD16×Dic67 | C2 | semidirect |
| 10. #16863446 | C2 | semidirect |
| 14. #14524042 | C22 | semidirect |
| 15. #14524041 | C22 | semidirect |
| 19. Q8×Dic67 | C22 | semidirect |
| 21. #14524008 | C22 | semidirect |
| 30. #14523975 | C22 | semidirect |
| 31. #14523974 | C22 | semidirect |
| 32. Dic67⋊C8 | C22 | semidirect |
| 33. #14523968 | C22 | semidirect |
| 34. #14523967 | C22 | semidirect |
| 37. C8×Dic67 | C22 | semidirect |
| 103. C2×Dic67 | SD16 | semidirect |
| 137. C67 | #3101 | semidirect |