A growing body of studies on systemic risk in financial markets has emphasized the key importance of taking into consideration the complex interconnections among financial institutions. Much effort has been put into modeling the contagion dynamics of financial shocks and into assessing the resilience of specific financial markets, either using real network data, reconstruction techniques or simple toy networks. Here, we address the more general problem of how shock propagation dynamics depend on the topological details of the underlying network. To this end, we consider different realistic network topologies, all consistent with balance sheet information obtained from real data on financial institutions. In particular, we consider networks of varying density and with different block structures. In addition, we diversify in the details of the shock propagation dynamics.We confirm that the systemic risk properties of a financial network are extremely sensitive to its network features. Our results can aid in the design of regulatory policies to improve the robustness of financial markets.