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×M16×D67 | C2 | semidirect |
| 2. #16863903 | C2 | semidirect |
| 3. C2×#14524014 | C2 | semidirect |
| 4. #16863646 | C2 | semidirect |
| 5. #16863639 | C2 | semidirect |
| 6. #16863629 | C2 | semidirect |
| 7. #16863622 | C2 | semidirect |
| 8. #16863438 | C2 | semidirect |
| 9. #16863401 | C2 | semidirect |
| 10. #16863397 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C67 | C2 | semidirect |
| 15. C2×#11761611 | C22 | semidirect |
| 17. C2×C8×D67 | C22 | semidirect |
| 19. #14524019 | C22 | semidirect |
| 20. #14524019 | C22 | semidirect |
| 25. #14524014 | C22 | semidirect |
| 26. #14524014 | C22 | semidirect |
| 33. #14523977 | C22 | semidirect |
| 34. #14523975 | C22 | semidirect |
| 35. #14523967 | C22 | semidirect |
| 36. #14523964 | C22 | semidirect |
| 37. #14523964 | C22 | semidirect |
| 38. #14523964 | C22 | semidirect |
| 42. C2×SD16×C67 | C22 | semidirect |
| 43. C2×D8×C67 | C22 | semidirect |
| 91. M16×C67 | D4 | semidirect |
| 135. C8×C67 | C2×D4 | semidirect |
| 154. C2×D67 | AGL(1,ℤ/8) | semidirect |
| 173. C67 | #3055 | semidirect |
| 174. C2×AGL(1,ℤ/8) | D67 | semidirect |
| 190. C2×SD16 | C2×D67 | semidirect |
| 191. C2×D8 | C2×D67 | semidirect |
| 248. M16 | C22⋊D67 | semidirect |
| 309. C8 | C2×C22⋊D67 | semidirect |