Double-differential neutron yields from 400 MeV/nucleon 56Fe stopping in C, Al, Cu, and Pb targets are reported, along with Particle and Heavy Ion Transport Code System (PHITS) transport model calculations of the data. The yields were measured at 90, 120, and 160 deg in all four systems. Neutron energies were measured from 1 to 2 MeV up to a few hundred mega-electron-volts. The data augment previous measurements made by Kurosawa et al. that were reported for angles between 0 and 90 deg. The measurements for each target were made at two different target orientations, resulting in two different thicknesses of target that neutrons had to traverse before reaching the neutron detectors. The differences in the spectra between two different target orientations are due to neutron transport through the target and as such provide an interesting test of transport model calculations. The data indicate that PHITS reproduces the effects of neutron transport very well but may overestimate neutron production between energies of 10 to 50 MeV in some cases.