Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16863788 | C2 | semidirect |
| 3. #16863770 | C2 | semidirect |
| 4. #16863762 | C2 | semidirect |
| 5. #16863753 | C2 | semidirect |
| 6. #16863618 | C2 | semidirect |
| 7. #16863596 | C2 | semidirect |
| 8. #16863556 | C2 | semidirect |
| 9. #16863546 | C2 | semidirect |
| 10. #16863457 | C2 | semidirect |
| 11. #541×C67 | C2 | semidirect |
| 14. C2×#11761618 | C22 | semidirect |
| 17. C2×#11761615 | C22 | semidirect |
| 24. C4⋊(C67⋊C8) | C22 | semidirect |
| 25. #14523966 | C22 | semidirect |
| 28. #14523963 | C22 | semidirect |
| 30. #14523954 | C22 | semidirect |
| 31. C4×C67⋊C8 | C22 | semidirect |
| 32. C4⋊Q8×C67 | C22 | semidirect |
| 35. #125×C67 | C22 | semidirect |
| 37. C4×Q8×C67 | C22 | semidirect |
| 123. C67 | #3222 | semidirect |
| 124. #541 | D67 | semidirect |
| 141. C4⋊Q8 | C2×D67 | semidirect |
| 146. #125 | C2×D67 | semidirect |
| 152. C4×Q8 | C2×D67 | semidirect |