The single-bond cZt-tZt isomerization rate constants of 1,3,5-cis-hexatriene dissolved in a series of explicit alkane (cydohexane, n-heptane, and cycloheptane) and alcohol (methanol, ethanol, and n-propanol) solvents were calculated via reactive flux theory, from classical molecular dynamics simulations, at different temperatures (275-325 K). We find that the isomerization rate constants in alcohol solvents are slower than those in alkane solvents, in accord with the observed experimental trend (Harris, D. A.; Orozco, M. B.; Sension, R. J. J. Phys. Chem. A 2006, 110, 9325-9333). We also find that the same trend is obtained when the transition state theory limit of the reactive flux expression for the reaction rate constant is employed. The solvent dependence of the reaction rate constant is then traced back to the fundamentally different structure of the solvation shell in alcohol and alkane solvents. Whereas in alcohol solvents, hexatriene fits inside a rigid cavity formed by the hydrogen-bonded network, which is relatively insensitive to conformational dynamics, alkane solvents form a cavity around hexatriene that adjusts to the conformational state of hexatriene, thereby increasing the entropy of transition state configurations relative to reactant configurations and giving rise to faster isomerization.