On recognition by spectrum of the simple groups $B_3(q)$, $C_3(q)$, and $D_4(q)$

The spectrum of a finite group is the set of its element orders. Two groups are isospectral whenever they have the same spectra. We consider the classes of finite groups isospectral to the simple symplectic and orthogonal groups $B_3(q)$, $C_3(q)$, and $D_4(q)$. We prove that in the case of even characteristic and $q>2$ these groups can be reconstructed from their spectra up to isomorphisms. In the case of odd characteristic we obtain a restriction on the composition structure of groups of this class.