Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
414 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 121 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. #16863734 | C2 | semidirect |
| 3. #16863731 | C2 | semidirect |
| 4. #16863714 | C2 | semidirect |
| 5. #16863652 | C2 | semidirect |
| 6. #16863644 | C2 | semidirect |
| 7. #16863556 | C2 | semidirect |
| 8. #16863552 | C2 | semidirect |
| 9. #16863535 | C2 | semidirect |
| 10. #16863360 | C2 | semidirect |
| 11. C2×C22⋊Q8×C67 | C2 | semidirect |
| 13. C2×#11761618 | C22 | semidirect |
| 14. C2×#11761615 | C22 | semidirect |
| 25. #14523976 | C22 | semidirect |
| 26. #14523974 | C22 | semidirect |
| 27. #14523967 | C22 | semidirect |
| 28. #14523967 | C22 | semidirect |
| 29. #14523966 | C22 | semidirect |
| 30. #14523963 | C22 | semidirect |
| 150. C67 | #3196 | semidirect |
| 152. C2×C22⋊Q8 | D67 | semidirect |