Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 442 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 |
|---|---|---|
| 1. #16863960 | C2 | semidirect |
| 2. #16863720 | C2 | semidirect |
| 3. #16863717 | C2 | semidirect |
| 4. #16863647 | C2 | semidirect |
| 5. #16863630 | C2 | semidirect |
| 6. #16863530 | C2 | semidirect |
| 7. #16863529 | C2 | semidirect |
| 8. #16863363 | C2 | semidirect |
| 9. #535×C67 | C2 | semidirect |
| 10. C22×D268 | C22 | semidirect |
| 13. C2×#11761612 | C22 | semidirect |
| 14. C22×C67⋊C8 | C22 | semidirect |
| 18. #14524017 | C22 | semidirect |
| 21. #14524002 | C22 | semidirect |
| 22. #14523976 | C22 | semidirect |
| 23. #14523974 | C22 | semidirect |
| 24. #14523964 | C22 | semidirect |
| 25. #14523964 | C22 | semidirect |
| 26. #14523963 | C22 | semidirect |
| 27. #14523963 | C22 | semidirect |
| 28. C22⋊(C67⋊C8) | C22 | semidirect |
| 29. C22⋊(C67⋊C8) | C22 | semidirect |
| 31. C22×D4×C67 | C22 | semidirect |
| 35. #121×C67 | C22 | semidirect |
| 38. #117×C67 | C22 | semidirect |
| 145. C67 | #3199 | semidirect |
| 147. #535 | D67 | semidirect |
| 157. C22×D4 | C2×D67 | semidirect |
| 169. #121 | C2×D67 | semidirect |
| 175. #117 | C2×D67 | semidirect |