Let the three sides of a triangle \( ABC \) be given by the vectors \( 2\hat{i}-\hat{j}+ \hat{k} \), \( \hat{i}-3\hat{j}-5\hat{k} \) and \( 3\hat{i}-4\hat{j}-4\hat{k} \). Let \( G \) be the centroid of the triangle \( ABC \). Then \( 6 \left( |\overline{AG}|^2 + |\overline{BG}|^2 + |\overline{CG}|^2 \right) \) is equal to ________________.
