In spite of his "surprise ending," with whom does Browning seem to sympathize most? the Duke the Duchess

In Browning's poem, "My Last Duchess," the Duke was married to his lovely wife, the Duchess, whose painting he has on the wall of his castle and is showing it to a visitor. As we read the poem, we find out that the Duchess liked to flirt a lot with other men which is why the Duke had her killed. I'm not sure who Browning seems to sympathize with - I guess the Duchess, given that she was murdered. The Duke is not the one who should be sympathized with.