Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16863907 | C2 | semidirect |
| 2. #16863731 | C2 | semidirect |
| 3. #16863717 | C2 | semidirect |
| 4. #16863714 | C2 | semidirect |
| 5. #16863630 | C2 | semidirect |
| 6. #16863623 | C2 | semidirect |
| 7. #16863547 | C2 | semidirect |
| 8. #16863539 | C2 | semidirect |
| 9. #16863530 | C2 | semidirect |
| 10. C2×C22⋊(C67⋊C8) | C2 | semidirect |
| 11. C2×#121×C67 | C2 | semidirect |
| 12. C2×#11761628 | C22 | semidirect |
| 13. C2×#11761616 | C22 | semidirect |
| 14. C2×#11761613 | C22 | semidirect |
| 15. C22×C67⋊C8 | C22 | semidirect |
| 18. #14524022 | C22 | semidirect |
| 20. #14524017 | C22 | semidirect |
| 24. #14524002 | C22 | semidirect |
| 25. #14523976 | C22 | semidirect |
| 26. #14523974 | C22 | semidirect |
| 27. #14523966 | C22 | semidirect |
| 28. #14523964 | C22 | semidirect |
| 29. #14523964 | C22 | semidirect |
| 30. #14523963 | C22 | semidirect |
| 33. C22⋊(C67⋊C8) | C22 | semidirect |
| 159. C67 | #3188 | semidirect |
| 161. C2×#121 | D67 | semidirect |