Crystallographic and magnetic structures of the cubic NaZn₁₃-type intermetallic compound LaFe_11.4Si_1.6 have been studied by means of powder neutron diffraction. Rietveld analysis indicates that Si atoms substitute for Fe atoms randomly on two different Fe sites. All spins in the unit cell are aligned ferromagnetically with the Fe^I (8b) moment smaller than the Fe^II (96i) one. The long-range ferromagnetic ordering induces a drastic expansion of the lattice and the coexistence of the large and small volume phases near the Curie temperature. Even in the ferromagnetic state, the lattice expansion still correlates strongly with the spontaneous magnetic moment, marked by a large positive magnetovolume coupling constant kC = 1.14 × 10^-8 cm⁶ emu^-2. From the temperature dependence of Fe-Fe bond lengths, we suggest that the Fe-Fe exchange interaction between the clusters (each formed by a central Fe^I atom and 12 surrounding Fe^II atoms) plays an important role in the magnetic properties of La(Fe_1-xAl/Si_x)₁₃, as does that within the clusters.