Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #16864024 | C2 | semidirect |
| 2. #16863760 | C2 | semidirect |
| 3. #16863755 | C2 | semidirect |
| 4. #16863750 | C2 | semidirect |
| 5. #16863742 | C2 | semidirect |
| 6. #16863401 | C2 | semidirect |
| 7. #16863397 | C2 | semidirect |
| 8. #16863392 | C2 | semidirect |
| 9. C2×#14523964 | C2 | semidirect |
| 10. #16863352 | C2 | semidirect |
| 14. #14524043 | C22 | semidirect |
| 16. #14524035 | C22 | semidirect |
| 21. #14523967 | C22 | semidirect |
| 22. #14523967 | C22 | semidirect |
| 23. #14523967 | C22 | semidirect |
| 28. #14523964 | C22 | semidirect |
| 29. #14523964 | C22 | semidirect |
| 30. #14523964 | C22 | semidirect |
| 31. #14523954 | C22 | semidirect |
| 32. C4×C67⋊C8 | C22 | semidirect |
| 136. C67 | #3136 | semidirect |