  We compute the complete Fadell-Husseini index of the 8 element dihedral group
D_8 acting on S^d \times S^d, both for F_2 and for integer coefficients. This
establishes the complete goup cohomology lower bounds for the two hyperplane
case of Gr"unbaum's 1960 mass partition problem: For which d and j can any j
arbitrary measures be cut into four equal parts each by two suitably-chosen
hyperplanes in R^d? In both cases, we find that the ideal bounds are not
stronger than previously established bounds based on one of the maximal abelian
subgroups of D_8.
