Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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. #16863927 | C2 | semidirect |
| 2. C2×#14524030 | C2 | semidirect |
| 3. #16863779 | C2 | semidirect |
| 4. #16863749 | C2 | semidirect |
| 5. #16863617 | C2 | semidirect |
| 6. #16863609 | C2 | semidirect |
| 7. #16863554 | C2 | semidirect |
| 8. #16863547 | C2 | semidirect |
| 9. #16863534 | C2 | semidirect |
| 10. #16863446 | C2 | semidirect |
| 13. C2×Dic268 | C22 | semidirect |
| 15. C2×#11761616 | C22 | semidirect |
| 17. #14524034 | C22 | semidirect |
| 22. #14524030 | C22 | semidirect |
| 25. #14524008 | C22 | semidirect |
| 27. D4×Dic67 | C22 | semidirect |
| 32. Dic67⋊C8 | C22 | semidirect |
| 33. #14523968 | C22 | semidirect |
| 34. #14523966 | C22 | semidirect |
| 37. C8×Dic67 | C22 | semidirect |
| 144. C67 | #3211 | semidirect |