Symmetric (70,24,8) designs having Frob21 × Z2 as an automorphism group

Up to isomorphism there are twenty-two symmetric (70,24,8) designs having automorphism group isomorphic to Frob21 × Z2. Among them there are four self-dual, and nine pairs of dual designs. Full automorphism groups of those designs are isomorphic to Frob21 × Z2. Designs are constructed by means of tactical decompositions, using a principal series of the group Frob21 × Z2