The fragmentation of the hydronium cation ${\text{H}}_{3}{\text{O}}^{+}$ after photoabsorption at 13.5 nm has been investigated with a crossed-photon-and-ion-beams experiment making pulsing and trapping techniques available for fragment momentum imaging at the intense Free-electron LASer in Hamburg. The observed photofragmentation patterns demonstrate that the photolysis of ${\text{H}}_{3}{\text{O}}^{+}$ proceeds by valence ionization into ${\text{H}}_{3}{\text{O}}^{2+}$ which subsequently fragments to mainly $\text{OH}+2{\text{H}}^{+}$ and ${\text{H}}_{2}{\text{O}}^{+}+{\text{H}}^{+}$ with a branching ratio of up to 0.6:1 and with different degrees of excitation of the molecular fragment. The cross section for fragmentation into $\text{OH}+2{\text{H}}^{+}$ is found to be $(0.37\ifmmode\pm\else\textpm\fi{}0.18)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}\text{ }{\text{cm}}^{2}$, while the total photoabsorption cross section is estimated to be greater than $0.95\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}\text{ }{\text{cm}}^{2}$. The data suggest that ionization mainly occurs from the $3{a}_{1}$ and $1e$ valence orbitals and that initial ionization from $3{a}_{1}$ mainly leads to fragmentation into ${\text{H}}_{2}{\text{O}}^{+}(A\text{ }{^{2}A}_{1})+{\text{H}}^{+}$ while initial ionization from the $1e$ orbital predominantly populates the ${\text{H}}_{2}{\text{O}}^{+}(B\text{ }{^{2}B}_{2})+{\text{H}}^{+}$ and $\text{OH}(X^{2}\ensuremath{\Pi})+2{\text{H}}^{+}$ channels. The results are of significance for astrophysical models of gas clouds in the vicinity of hot radiating objects and for models of the chemistry of planetary and lunar ionospheres under solar irradiation.