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. #16863932 | C2 | semidirect |
| 2. C2×D4×Dic67 | C2 | semidirect |
| 3. #16863724 | C2 | semidirect |
| 4. #16863710 | C2 | semidirect |
| 5. #16863694 | C2 | semidirect |
| 6. #16863613 | C2 | semidirect |
| 8. #16863505 | C2 | semidirect |
| 9. #16863497 | C2 | semidirect |
| 10. #16863450 | C2 | semidirect |
| 11. #450×C67 | C2 | semidirect |
| 15. #14524034 | C22 | semidirect |
| 16. #14524032 | C22 | semidirect |
| 19. Q8×Dic67 | C22 | semidirect |
| 24. #14524005 | C22 | semidirect |
| 30. #14523977 | C22 | semidirect |
| 31. #14523974 | C22 | semidirect |
| 32. Dic67⋊C8 | C22 | semidirect |
| 33. #14523967 | C22 | semidirect |
| 34. #14523965 | C22 | semidirect |
| 37. #14523953 | C22 | semidirect |
| 141. C67 | #3114 | semidirect |
| 148. #450 | D67 | semidirect |