Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 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. #16864027 | C2 | semidirect |
| 3. #16863759 | C2 | semidirect |
| 4. #16863754 | C2 | semidirect |
| 5. #16863749 | C2 | semidirect |
| 6. #16863741 | C2 | semidirect |
| 7. #16863401 | C2 | semidirect |
| 8. #16863395 | C2 | semidirect |
| 9. #16863393 | C2 | semidirect |
| 10. #16863351 | C2 | semidirect |
| 11. C2×#102×C67 | C2 | semidirect |
| 15. #14524042 | C22 | semidirect |
| 18. #14524034 | C22 | semidirect |
| 26. #14523968 | C22 | semidirect |
| 27. #14523968 | C22 | semidirect |
| 28. #14523966 | C22 | semidirect |
| 29. #14523965 | C22 | semidirect |
| 30. #14523965 | C22 | semidirect |
| 33. #14523963 | C22 | semidirect |
| 34. #14523953 | C22 | semidirect |
| 35. C8×Dic67 | C22 | semidirect |
| 136. C67 | #3136 | semidirect |
| 146. C2×#102 | D67 | semidirect |