The total of 22 2-designs on 18 points have been found. All these designs have the same group as an automorphism group. This group can be represented as the wreath product of G and H, where G denotes the subgroup of order 3 of PSL(2,2) and H denotes the subgroup of order 12 of PSL(2,5). The 2-(18,7,42·s) designs for s 2 {15, 19, 25, 27, 30, 37, 38, 50} and the 2-(18,8,28·s) designs for s 2 {27, 44, 46, 48, 50, 53, 54, 57, 59, 61, 73, 77, 80, 81} have been detected. Up to our knowledge, 16 of these 22 found designs are new.