Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #16864210 | C2 | semidirect |
| 2. #16864197 | C2 | semidirect |
| 3. #16863839 | C2 | semidirect |
| 4. #16863835 | C2 | semidirect |
| 5. #16863830 | C2 | semidirect |
| 6. #16863826 | C2 | semidirect |
| 7. #16863825 | C2 | semidirect |
| 8. C2×#14523987 | C2 | semidirect |
| 9. SD32×D67 | C2 | semidirect |
| 10. #16863814 | C2 | semidirect |
| 11. #509×C67 | C2 | semidirect |
| 20. #14524062 | C22 | semidirect |
| 21. C2×Dic268 | C22 | semidirect |
| 22. Q16×D67 | C22 | semidirect |
| 25. Dic536 | C22 | semidirect |
| 26. #14523989 | C22 | semidirect |
| 27. #14523988 | C22 | semidirect |
| 28. #14523987 | C22 | semidirect |
| 29. #14523987 | C22 | semidirect |
| 30. #14523987 | C22 | semidirect |
| 31. #14523986 | C22 | semidirect |
| 32. #14523984 | C22 | semidirect |
| 33. #14523982 | C22 | semidirect |
| 34. C2×C67⋊C16 | C22 | semidirect |
| 35. C16×D67 | C22 | semidirect |
| 36. #135×C67 | C22 | semidirect |
| 38. SD32×C67 | C22 | semidirect |
| 39. D16×C67 | C22 | semidirect |
| 40. M32×C67 | C22 | semidirect |
| 127. C67 | #3416 | semidirect |
| 133. #509 | D67 | semidirect |
| 148. #135 | C2×D67 | semidirect |
| 161. SD32 | C2×D67 | semidirect |
| 163. D16 | C2×D67 | semidirect |
| 165. M32 | C2×D67 | semidirect |