Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#11761616 | C2 | semidirect |
| 3. #16863972 | C2 | semidirect |
| 4. #16863611 | C2 | semidirect |
| 5. #16863601 | C2 | semidirect |
| 6. #16863423 | C2 | semidirect |
| 7. #16863404 | C2 | semidirect |
| 8. #16863390 | C2 | semidirect |
| 9. #518×C67 | C2 | semidirect |
| 19. #14524043 | C22 | semidirect |
| 20. #14524031 | C22 | semidirect |
| 23. C4⋊(C67⋊C8) | C22 | semidirect |
| 24. #14523966 | C22 | semidirect |
| 25. #14523966 | C22 | semidirect |
| 26. #14523963 | C22 | semidirect |
| 117. C67 | #3042 | semidirect |
| 121. #518 | D67 | semidirect |