Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
410 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16863930 | C2 | semidirect |
| 2. #16863802 | C2 | semidirect |
| 3. #16863783 | C2 | semidirect |
| 4. #16863760 | C2 | semidirect |
| 5. #16863758 | C2 | semidirect |
| 6. #16863630 | C2 | semidirect |
| 7. #16863623 | C2 | semidirect |
| 8. #16863506 | C2 | semidirect |
| 9. #16863496 | C2 | semidirect |
| 10. C2×#14523954 | C2 | semidirect |
| 11. #532×C67 | C2 | semidirect |
| 110. C67⋊C8 | #41 | semidirect |
| 138. C67 | #3180 | semidirect |
| 139. #532 | D67 | semidirect |