Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 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. #16863734 | C2 | semidirect |
| 3. #16863720 | C2 | semidirect |
| 4. #16863644 | C2 | semidirect |
| 5. #16863627 | C2 | semidirect |
| 6. #16863546 | C2 | semidirect |
| 7. #16863535 | C2 | semidirect |
| 8. #16863363 | C2 | semidirect |
| 9. #536×C67 | C2 | semidirect |
| 13. C2×#11761612 | C22 | semidirect |
| 14. C22×C67⋊C8 | C22 | semidirect |
| 22. #14523976 | C22 | semidirect |
| 23. #14523974 | C22 | semidirect |
| 24. #14523967 | C22 | semidirect |
| 25. #14523967 | C22 | semidirect |
| 29. C22⋊(C67⋊C8) | C22 | semidirect |
| 31. C22×Q8×C67 | C22 | semidirect |
| 37. C22⋊Q8×C67 | C22 | semidirect |
| 38. #117×C67 | C22 | semidirect |
| 138. C67 | #3200 | semidirect |
| 139. #536 | D67 | semidirect |
| 149. C22×Q8 | C2×D67 | semidirect |
| 162. C22⋊Q8 | C2×D67 | semidirect |
| 168. #117 | C2×D67 | semidirect |