Deviations from Fourier's law emerge from numerical simulations of various lattices modelling solids. Non-integrability and moreover chaotic motion are considered to be conditions of normal heat conduction. However, these are not sufficient conditions. Using a simple model as an example, we show that non-diffusive transport could occur even in the presence of disorder in the lattice and completely chaotic dynamics. We conclude that diffusive and non-diffusive transport can coexist, while the system is moving along a chaotic trajectory in the phase space.