  We study the competition between two different topological orders in three
dimensions by considering the X-cube model and the three-dimensional toric
code. The corresponding Hamiltonian can be decomposed into two commuting parts,
one of which displays a self-dual spectrum. To determine the phase diagram, we
compute the high-order series expansions of the ground-state energy in all
limiting cases. Apart from the topological order related to the toric code and
the fractonic order related to the X-cube model, we found two new phases which
are adiabatically connected to classical limits with nontrivial sub-extensive
degeneracies. All phase transitions are found to be first order.
