  We investigate statistical properties of the distribution of matter at
redshift zero in disformal gravity by using N-body simulations. The disformal
model studied here consists of a conformally coupled symmetron field with an
additional exponential disformal term. We conduct cosmological simulations to
discover the impact of the new disformal terms in the matter power spectrum,
halo mass function, and radial profile of the scalar field. We calculated the
disformal geodesic equation and the equation of motion for the scalar field. We
then implemented these equations into the N-body code ISIS, which is a modified
gravity version of the code RAMSES. The presence of a conformal symmetron field
increases both the power spectrum and mass function compared to standard
gravity on small scales. Our main finding is that the newly added disformal
terms tend to counteract these effects and can make the evolution slightly
closer to standard gravity. We finally show that the disformal terms give rise
to oscillations of the scalar field in the centre of the dark matter haloes.
