The classical triangular antiferromagnetic Heisenberg model with Dzyaloshinskii-Moriya interactions in a magnetic field is studied. We focus in particular on the emergence of a composite spin crystal phase that was recently observed in [Phys. Rev. B 92, 214439 (2015)] for intermediate fields. This complex phase, which corresponds to a lattice of Z2 vortices, can be made up from three inter-penetrated skyrmion lattices, one for each sub-lattice of the original triangular one. We present our numerical results and the explicit construction of the low-energy effective action that reproduces the correct phenomenology. This effective action could serve as a starting point to study the coupling to charge carriers, lattice vibrations, structural disorder and transport phenomena.