Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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×D8×D67 | C2 | semidirect |
| 2. C2×#14524051 | C2 | semidirect |
| 3. #16863962 | C2 | semidirect |
| 4. #16863650 | C2 | semidirect |
| 5. #16863649 | C2 | semidirect |
| 6. #16863646 | C2 | semidirect |
| 7. #16863631 | C2 | semidirect |
| 8. #16863630 | C2 | semidirect |
| 9. #16863431 | C2 | semidirect |
| 10. #16863399 | C2 | semidirect |
| 11. #469×C67 | C2 | semidirect |
| 19. C2×#11761611 | C22 | semidirect |
| 20. C22×C67⋊C8 | C22 | semidirect |
| 22. C2×C8×D67 | C22 | semidirect |
| 25. #14524018 | C22 | semidirect |
| 26. #14524017 | C22 | semidirect |
| 27. #14524014 | C22 | semidirect |
| 31. #14523976 | C22 | semidirect |
| 32. #14523975 | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 34. #14523964 | C22 | semidirect |
| 35. #14523963 | C22 | semidirect |
| 37. C2×M16×C67 | C22 | semidirect |
| 38. #121×C67 | C22 | semidirect |
| 39. #106×C67 | C22 | semidirect |
| 40. #102×C67 | C22 | semidirect |
| 65. C8×D67 | D4 | semidirect |
| 147. C67 | #3058 | semidirect |
| 154. #469 | D67 | semidirect |
| 168. C2×M16 | C2×D67 | semidirect |
| 177. #121 | C2×D67 | semidirect |
| 183. #106 | C2×D67 | semidirect |
| 187. #102 | C2×D67 | semidirect |