  Given an elliptic curve $E/\mathbb{Q}$ with torsion subgroup $G =
E(\mathbb{Q})_{\rm tors}$ we study what groups (up to isomorphism) can occur as
the torsion subgroup of $E$ base-extended to $K$, a degree 6 extension of
$\mathbb{Q}$. We also determine which groups $H = E(K)_{\rm tors}$ can occur
infinitely often and which ones occur for only finitely many curves. This
article is a first step towards a complete classification of torsion growth of
over sextic fields.
