In this article we consider the class QSLpc qc r;1 4 of all real quadratic differential systems dx dt = p(x; y), dy dt = q(x; y) with gcd(p; q) = 1, having invariant lines of total multiplicity four and one real and two complex infinite singularities. We construct compactified canonical forms for this class and bifurcation diagrams for these compactified canonical forms. These diagrams contain many repetitions of phase portraits due to symmetries under the action of the group of affine transformations and time homotheties. We construct the orbit spaces under this action and the corresponding bifurcation diagrams in these orbit spaces. These diagrams retain only the essence of the dynamics and thus make transparent their content.