Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16864008 | C2 | semidirect |
| 2. #16863791 | C2 | semidirect |
| 3. #16863768 | C2 | semidirect |
| 4. #16863760 | C2 | semidirect |
| 5. #16863750 | C2 | semidirect |
| 6. #16863615 | C2 | semidirect |
| 7. #16863593 | C2 | semidirect |
| 8. #16863558 | C2 | semidirect |
| 9. #16863547 | C2 | semidirect |
| 10. #16863457 | C2 | semidirect |
| 12. C2×#11761618 | C22 | semidirect |
| 15. C2×#11761616 | C22 | semidirect |
| 16. #14524043 | C22 | semidirect |
| 18. #14524035 | C22 | semidirect |
| 21. C4×Dic134 | C22 | semidirect |
| 22. C4⋊(C67⋊C8) | C22 | semidirect |
| 23. #14523967 | C22 | semidirect |
| 26. #14523964 | C22 | semidirect |
| 28. #14523954 | C22 | semidirect |
| 29. C4×C67⋊C8 | C22 | semidirect |
| 123. C67 | #3222 | semidirect |