Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14524068 | C2 | semidirect |
| 2. C22×#11761613 | C2 | semidirect |
| 3. #16863870 | C2 | semidirect |
| 4. #16863608 | C2 | semidirect |
| 5. #16863588 | C2 | semidirect |
| 6. #16863423 | C2 | semidirect |
| 7. #16863401 | C2 | semidirect |
| 8. #16863392 | C2 | semidirect |
| 9. #535×C67 | C2 | semidirect |
| 12. C2×#11761615 | C22 | semidirect |
| 15. C2×#11761613 | C22 | semidirect |
| 18. C4×D268 | C22 | semidirect |
| 22. C4⋊(C67⋊C8) | C22 | semidirect |
| 23. #14523967 | C22 | semidirect |
| 24. #14523964 | C22 | semidirect |
| 25. #14523964 | C22 | semidirect |
| 28. #127×C67 | C22 | semidirect |
| 29. #124×C67 | C22 | semidirect |
| 36. C2×D268 | D4 | semidirect |
| 122. C67 | #3041 | semidirect |
| 125. #535 | D67 | semidirect |
| 142. #127 | C2×D67 | semidirect |
| 143. #124 | C2×D67 | semidirect |