We construct a supersymmeterized version of the model presented by Grimus and Lavoura (GL) in [1] which predicts theta_{23} maximal and theta_{13}=0 in the lepton sector. For this purpose, we extend the flavor group, which is D4 x Z2^{(aux)} in the original model, to D4 x Z5. An additional difference is the absence of right-handed neutrinos. Despite these changes the model is the same as the GL model, since theta_{23} maximal and theta_{13}=0 arise through the same mismatch of D4 subgroups, D2 in the charged lepton and Z2 in the neutrino sector. In our setup D4 is solely broken by gauge singlets, the flavons. We show that their vacuum structure, which leads to the prediction of theta_{13} and theta_{23}, is a natural result of the scalar potential. We find that the neutrino mass matrix only allows for inverted hierarchy, if we assume a certain form of spontaneous CP violation. The quantity |m_{ee}|, measured in neutrinoless double beta decay, is nearly equal to the lightest neutrino mass m3. The Majorana phases phi1 and phi2 are restricted to a certain range for m3 < 0.06 eV. We discuss the next-to-leading order corrections which give rise to shifts in the vacuum expectation values of the flavons. These induce deviations from maximal atmospheric mixing and vanishing theta_{13}. It turns out that these deviations are smaller for theta_{23} than for theta_{13}.
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