  The structure of $^{44}$S has been studied using delayed $\gamma$ and
electron spectroscopy at \textsc{ganil}. The decay rates of the 0$^+_2$
isomeric state to the 2$^+_1$ and 0$^+_1$ states have been measured for the
first time, leading to a reduced transition probability
B(E2~:~2$^{+}_1$$\rightarrow$0$^{+}_2)$= 8.4(26)~e$^2$fm$^4$ and a monopole
strength $\rho^2$(E0~:~0$^{+}_2$$\rightarrow$0$^{+}_1)$
=~8.7(7)$\times$10$^{-3}$. Comparisons to shell model calculations point
towards prolate-spherical shape coexistence and a phenomenological two level
mixing model is used to extract a weak mixing between the two configurations.
