... of orbits of PGL(2,q). There are some knownresults on 3-designs from PGL(2,q) in the literature, see for example [1, 4, 6]. In thispaper, we first determine the sizes of orbits from the actions ... in the above formula.7 Orbit sizes and 3-designs from PGL(2,q)We use the results of the previous sections to show the existence of a large number of new 3-designs. First we state the following ... Since PGL(2,q)isa subgroup of PSL(2,q2) and it has a unique subgroup PSL(2,q), we can easily extract allnecessary information concerning the subgroups of PGL(2,q) and their overgroups from the...