Field-induced structure formation in a ferrofluid with well-defined magnetite nanoparticles with a permanent magnetic dipole moment was studied with small-angle neutron scattering (SANS) as a function of the magnetic interactions. The interactions were tuned by adjusting the size of the well-defined, single-magnetic-domain magnetite (Fe3O4) particles and by applying an external magnetic field. For decreasing particle dipole moments, the data show a progressive distortion of the hexagonal symmetry, resulting from the formation of magnetic sheets. The SANS data show qualitative agreement with recent cryogenic transmission electron microscopy results obtained in 2D [Klokkenburg, Phys. Rev. Lett. 97, 185702 (2006)] on the same ferrofluids.