All nonisomorphic \(2\)-\((21, 6, 3)\) designs with automorphisms of order \(7\) or \(5\) were found, and the orders of their groups of automorphisms were determined. There are \(33\) nonisomorphic \(2\)-\((21, 6, 3)\) designs with automorphisms of order \(7\) and \(203\) with automorphisms of order \(5\).