On finite groups isospectral to the simple group $S_4(3)$

The spectrum of a finite group is the set of its element orders. A finite group $G$ is called critical with respect to a subset $\omega$ of natural numbers if $\omega$ coincides with the spectrum of $G$ and does not coincide with the spectra of proper sections of $G$. We study the structure of finite groups with the same spectrum as the simple symplectic group $PSp(4, 3)$. In particular, we describe groups critical with respect to the spectrum of $PSp(4, 3)$.