Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #16863876 | C2 | semidirect |
| 3. #16863719 | C2 | semidirect |
| 4. #16863718 | C2 | semidirect |
| 5. #16863713 | C2 | semidirect |
| 6. #16863708 | C2 | semidirect |
| 7. #16863438 | C2 | semidirect |
| 8. #16863432 | C2 | semidirect |
| 9. C2×#14523964 | C2 | semidirect |
| 10. #16863364 | C2 | semidirect |
| 11. #418×C67 | C2 | semidirect |
| 23. #14524001 | C22 | semidirect |
| 25. C4⋊C4×D67 | C22 | semidirect |
| 26. #14523977 | C22 | semidirect |
| 27. #14523976 | C22 | semidirect |
| 28. #14523976 | C22 | semidirect |
| 29. #14523975 | C22 | semidirect |
| 30. #14523974 | C22 | semidirect |
| 31. #14523974 | C22 | semidirect |
| 34. (C2×D67)⋊C8 | C22 | semidirect |
| 35. (C2×D67)⋊C8 | C22 | semidirect |
| 135. C67 | #3096 | semidirect |
| 144. #418 | D67 | semidirect |