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×#14524069 | C2 | semidirect |
| 2. C2×#14524050 | C2 | semidirect |
| 3. #16863974 | C2 | semidirect |
| 4. #16863647 | C2 | semidirect |
| 5. #16863640 | C2 | semidirect |
| 6. #16863630 | C2 | semidirect |
| 7. #16863623 | C2 | semidirect |
| 8. #16863439 | C2 | semidirect |
| 9. #16863390 | C2 | semidirect |
| 10. C2×#14523964 | C2 | semidirect |
| 11. #535×C67 | C2 | semidirect |
| 18. C2×#11761612 | C22 | semidirect |
| 20. C22×C67⋊C8 | C22 | semidirect |
| 21. #14524022 | C22 | semidirect |
| 23. #14524017 | C22 | semidirect |
| 27. #14523976 | C22 | semidirect |
| 28. #14523974 | C22 | semidirect |
| 29. #14523966 | C22 | semidirect |
| 30. #14523966 | C22 | semidirect |
| 33. #14523963 | C22 | semidirect |
| 34. #14523963 | C22 | semidirect |
| 54. #11761612 | D4 | semidirect |
| 152. C67 | #3062 | semidirect |
| 156. #535 | D67 | semidirect |