Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14524051 | C2 | semidirect |
| 2. #16863974 | C2 | semidirect |
| 3. #16863963 | C2 | semidirect |
| 4. #16863646 | C2 | semidirect |
| 5. #16863639 | C2 | semidirect |
| 6. #16863629 | C2 | semidirect |
| 7. #16863622 | C2 | semidirect |
| 8. #16863438 | C2 | semidirect |
| 9. #16863392 | C2 | semidirect |
| 10. C2×#14523964 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C67 | C2 | semidirect |
| 14. C2×#11761611 | C22 | semidirect |
| 16. C2×C8×D67 | C22 | semidirect |
| 20. #14524019 | C22 | semidirect |
| 25. #14524014 | C22 | semidirect |
| 29. #14523977 | C22 | semidirect |
| 30. #14523975 | C22 | semidirect |
| 31. #14523967 | C22 | semidirect |
| 32. #14523967 | C22 | semidirect |
| 35. #14523964 | C22 | semidirect |
| 36. #14523964 | C22 | semidirect |
| 83. M16×C67 | D4 | semidirect |
| 152. C67 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D67 | semidirect |
| 220. M16 | C22⋊D67 | semidirect |