We explore the network topology arising from a dataset of the overnight interbank transactions on the e-MID trading platform from January 1999 to December 2010. In order to shed light on the hierarchical structure of the banking system, we estimate different versions of a core-periphery model. Our main findings are: (1) A core-periphery structure provides a better fit for these interbank data than alternative network models, (2) the identified core is quite stable over time, consisting of roughly 28% of all banks before the global financial crisis (GFC) and 23% afterwards, (3) the majority of core banks can be classified as intermediaries, i.e. as banks both borrowing and lending money, (4) allowing for asymmetric `coreness' with respect to lending and borrowing considerably improves the fit, and reveals more concentration in borrowing than lending activity of money center banks. During the financial crisis of 2008, the reduction of interbank lending was mainly due to core banks' reducing their numbers of active outgoing links.