Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 466 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 |
|---|---|---|
| 1. C2×#14524017 | C2 | semidirect |
| 2. #16863724 | C2 | semidirect |
| 3. #16863720 | C2 | semidirect |
| 4. #16863707 | C2 | semidirect |
| 5. #16863647 | C2 | semidirect |
| 6. #16863644 | C2 | semidirect |
| 7. #16863546 | C2 | semidirect |
| 8. #16863541 | C2 | semidirect |
| 9. #16863529 | C2 | semidirect |
| 10. #16863360 | C2 | semidirect |
| 11. #525×C67 | C2 | semidirect |
| 14. C2×#11761615 | C22 | semidirect |
| 15. C2×#11761613 | C22 | semidirect |
| 16. C2×#11761612 | C22 | semidirect |
| 23. #14523976 | C22 | semidirect |
| 24. #14523974 | C22 | semidirect |
| 25. #14523967 | C22 | semidirect |
| 26. #14523964 | C22 | semidirect |
| 27. #14523963 | C22 | semidirect |
| 28. #14523963 | C22 | semidirect |
| 31. C22⋊(C67⋊C8) | C22 | semidirect |
| 32. C2×#41×C67 | C22 | semidirect |
| 36. C22⋊Q8×C67 | C22 | semidirect |
| 38. #121×C67 | C22 | semidirect |
| 42. #117×C67 | C22 | semidirect |
| 159. C67 | #3194 | semidirect |
| 160. #525 | D67 | semidirect |
| 171. C2×#41 | C2×D67 | semidirect |
| 180. C22⋊Q8 | C2×D67 | semidirect |
| 186. #121 | C2×D67 | semidirect |
| 190. #117 | C2×D67 | semidirect |