  We map out the ground state phase diagram of the isotropic Kekul{\'e}-Kitaev
model on the honeycomb lattice in the presence of the Heisenberg exchange
couplings. Our study relies on large-scale tensor network simulations based on
graph-based projected entangled pair state (gPEPS) approach in the
thermodynamic limit. We find that on top of the quantum spin liquid (QSL) and
conventional magnetically ordered phases which are typical of the
Kitaev-Heisenberg model, the Kekul{\'e}-Heisenberg phase diagram, hosts two
plaquette valance bond solid (VBS) phases with vanishing magnetic order. While
the VBS phases preserve the symmetries of the original Hamiltonian, they differ
markedly from the Kitaev spin liquid by having decorated plaquette ordering
which is distinguished by a plaquette order parameter.
