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 |
|---|---|---|
| 2. #16863762 | C2 | semidirect |
| 3. #16863758 | C2 | semidirect |
| 4. #16863753 | C2 | semidirect |
| 5. #16863744 | C2 | semidirect |
| 6. #16863400 | C2 | semidirect |
| 7. #16863395 | C2 | semidirect |
| 8. #16863390 | C2 | semidirect |
| 9. C2×#14523963 | C2 | semidirect |
| 10. #16863352 | C2 | semidirect |
| 11. #544×C67 | C2 | semidirect |
| 21. #14523966 | C22 | semidirect |
| 22. #14523966 | C22 | semidirect |
| 23. #14523966 | C22 | semidirect |
| 28. #14523963 | C22 | semidirect |
| 29. #14523963 | C22 | semidirect |
| 30. #14523963 | C22 | semidirect |
| 31. #14523954 | C22 | semidirect |
| 32. C4×C67⋊C8 | C22 | semidirect |
| 34. C4⋊Q8×C67 | C22 | semidirect |
| 36. #125×C67 | C22 | semidirect |
| 136. C67 | #3136 | semidirect |
| 137. #544 | D67 | semidirect |
| 153. C4⋊Q8 | C2×D67 | semidirect |
| 156. #125 | C2×D67 | semidirect |