Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 328 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 |
|---|---|---|
| 2. #16863802 | C2 | semidirect |
| 3. #16863802 | C2 | semidirect |
| 4. #16863758 | C2 | semidirect |
| 5. #16863758 | C2 | semidirect |
| 6. #16863737 | C2 | semidirect |
| 8. #16863700 | C2 | semidirect |
| 9. #16863693 | C2 | semidirect |
| 10. #16863453 | C2 | semidirect |
| 11. #533×C67 | C2 | semidirect |
| 126. C67 | #3240 | semidirect |
| 127. #533 | D67 | semidirect |