A general sublaplacian is an operator of the form ${\rm div}_H(M {\rm grad}_H f)$ where ${\rm div}_H$ is a horizontal divergence, $M$ is a symmetric positive definite matrix acting on the horizontal bundle, and ${\rm grad}_H$ is a horizontal gradient. In the Euclidean setting one can always find a change of coordinates that brings such an operator into the standard form ${\rm div}({\rm grad}\, f)$ using the symmetric square root $C$ of $M$, however this is not always possible on a stratified group since $C$ must also extend to an automorphism of the Lie algebra of the group. If the group is free then extending $C$ to an automorphism is not a problem and the symmetric square root works. The second Heisenberg group is perhaps the simplest nonfree stratified group. In this case we employ a recently developed theory of horizontal jets to reveal that the classes of contact equivalent sublaplacians are uniquely determined by a positive real parameter.