We will present a flag-transitive large set of Desargues configurations invariant under the group \(\textrm{P}\Gamma \textrm{L}(2,9)\) of order 1440, which is isomorphic to the automorphism group of the symmetric group of degree 6. We will then classify all large sets of Desargues configurations. As it turns out, the flag-transitive example is the one with the largest possible symmetry group. In total, there are exactly 3617 pairwise non-isomorphic large sets of Desargues configurations.
