$Aut_0(\Lambda^2)$-symmetrical 4-extensions of the 2-dimensional grid $\Lambda^2$

Using an earlier proof by the author and V. I. Trofimov that there are only finitely many $Aut_0(\Lambda^2)$-symmetrical 4-extensions of the 2-dimensional grid $\Lambda^2$, we find all $Aut_0(\Lambda^2)$-symmetrical 4-extensions of grid $\Lambda^2$.