A degree d genus g cover of the complex projective line by a smooth irreducible curve C yields a vector bundle on the projective line by pushforward of the structure sheaf. We classify the bundles that arise this way when d = 6. Interestingly, our methods show that all constraints on the pushforward are "explained" by multiplication in an algebra. Finally, we show that all possible pushforwards are realized by covers with a nontrivial proper subcover.