Divisibility orders in $\beta N$

We consider five divisibility orders on the Stone-\v{C}ech compactification $\beta N$. We find antichains of incompatible elements, and characterize maximal and minimal elements. The main result shows that two of these relations, ${\mid }_L$ and ${\mid }_{LN}$, are strictly stronger than the Rudin-Keisler order.