A spin-1/2 Heisenberg model on a honeycomb lattice is investigated by doing triplon analysis and quantum Monte Carlo calculations. This model, inspired ${\mathrm{Cu}}_{2}{(\mathrm{pymca})}_{3}({\mathrm{ClO}}_{4}$), has three different antiferromagnetic exchange interactions (${J}_{A}, {J}_{B}, {J}_{C}$) sets of nearest-neighbor bonds which form kagome superlattice. While the bipartite unfrustra...