Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×#14524069 | C2 | semidirect |
| 2. #16863942 | C2 | semidirect |
| 3. C2×D4×Dic67 | C2 | semidirect |
| 4. #16863613 | C2 | semidirect |
| 5. #16863609 | C2 | semidirect |
| 6. #16863599 | C2 | semidirect |
| 7. #16863589 | C2 | semidirect |
| 8. #16863419 | C2 | semidirect |
| 9. #16863398 | C2 | semidirect |
| 10. #16863397 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C67 | C2 | semidirect |
| 18. #14524041 | C22 | semidirect |
| 19. #14524039 | C22 | semidirect |
| 20. #14524032 | C22 | semidirect |
| 21. #14524030 | C22 | semidirect |
| 33. Dic67⋊C8 | C22 | semidirect |
| 34. Dic67⋊C8 | C22 | semidirect |
| 35. #14523968 | C22 | semidirect |
| 36. #14523967 | C22 | semidirect |
| 37. #14523965 | C22 | semidirect |
| 38. #14523964 | C22 | semidirect |
| 84. C2×D4×C67 | D4 | semidirect |
| 158. Dic67 | AGL(1,ℤ/8) | semidirect |
| 167. C67 | #3036 | semidirect |
| 169. C2×AGL(1,ℤ/8) | D67 | semidirect |
| 226. C2×D4 | C22⋊D67 | semidirect |