Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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. #16863909 | C2 | semidirect |
| 2. C2×#14524018 | C2 | semidirect |
| 3. #16863723 | C2 | semidirect |
| 4. #16863714 | C2 | semidirect |
| 5. #16863633 | C2 | semidirect |
| 6. #16863628 | C2 | semidirect |
| 7. #16863546 | C2 | semidirect |
| 8. #16863544 | C2 | semidirect |
| 9. #16863532 | C2 | semidirect |
| 10. C22⋊C8×D67 | C2 | semidirect |
| 11. #484×C67 | C2 | semidirect |
| 12. C2×#11761629 | C22 | semidirect |
| 16. C2×#11761615 | C22 | semidirect |
| 17. C2×D536 | C22 | semidirect |
| 18. C2×C8×D67 | C22 | semidirect |
| 20. #14524019 | C22 | semidirect |
| 25. #14524018 | C22 | semidirect |
| 30. #14524001 | C22 | semidirect |
| 32. #14523974 | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 34. #14523963 | C22 | semidirect |
| 35. #14523963 | C22 | semidirect |
| 37. (C2×D67)⋊C8 | C22 | semidirect |
| 40. #107×C67 | C22 | semidirect |
| 41. #103×C67 | C22 | semidirect |
| 159. C67 | #3188 | semidirect |
| 162. #484 | D67 | semidirect |
| 193. #107 | C2×D67 | semidirect |
| 195. #103 | C2×D67 | semidirect |