Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
332 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 121 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. #16863795 | C2 | semidirect |
| 3. #16863753 | C2 | semidirect |
| 4. #16863737 | C2 | semidirect |
| 6. #16863688 | C2 | semidirect |
| 7. #16863683 | C2 | semidirect |
| 8. #16863678 | C2 | semidirect |
| 9. #16863673 | C2 | semidirect |
| 10. #16863449 | C2 | semidirect |
| 11. #533×C67 | C2 | semidirect |
| 130. C67 | #3233 | semidirect |
| 131. #533 | D67 | semidirect |