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 |
|---|---|---|
| 1. #16863967 | C2 | semidirect |
| 2. #16863737 | C2 | semidirect |
| 3. #16863717 | C2 | semidirect |
| 4. #16863640 | C2 | semidirect |
| 5. #16863623 | C2 | semidirect |
| 6. #16863547 | C2 | semidirect |
| 7. #16863534 | C2 | semidirect |
| 8. #16863363 | C2 | semidirect |
| 10. C22×Dic134 | C22 | semidirect |
| 13. C2×#11761612 | C22 | semidirect |
| 14. C22×C67⋊C8 | C22 | semidirect |
| 20. #14524022 | C22 | semidirect |
| 21. #14524002 | C22 | semidirect |
| 22. #14523976 | C22 | semidirect |
| 23. #14523974 | C22 | semidirect |
| 24. #14523966 | C22 | semidirect |
| 25. #14523966 | C22 | semidirect |
| 29. C22⋊(C67⋊C8) | C22 | semidirect |
| 138. C67 | #3200 | semidirect |