Deep minima in the transmission probability occur with periodicity _φ = 2π. Experimentally (where S is varied via the gate voltage at constant B) this would correspond to oscillations with periodicity _S = h/eB of Aharonov-Bohm oscillations in a single cavity. The 15 smaller oscillations between two deep minima have the periodicity of Aharonov-Bohm oscillations in the entire area covered by the 15 cavities. The observation of such faster oscillations shows that phase coherence is maintained in the experiment throughout the channel and thereby provides conclusive evidence for band structure in a lateral superlattice.