We present a detailed study of the geometric hyperplanes of the two generalized hexagons of order (2,2). This leads to concrete descriptions of th universal embeddings of these hexagons, as well as a description of theG2(2)-orbits on the Lie algebrag2(2), illustrating some of the anomalies of this algebra. As a byproduct of our investigations, we develop some general theory that can be applied to other incidence systems with 3 points per line.