By generalizing constructions in Kosaki (1994) and Kosaki and Longo, we will construct an AFD type III$_0$ factor with uncountably many non-conjugate subfactors such that (i) each subfactor has the same flow of weights as the ambient factor, and (ii) the principal and the dual principal graphs are of a specific form. We will deal with two cases: (a) the graphs are described by the Dynkin diagram $A_{4m-3}$, and (b) the graphs are the ones given by a pair of a group and its subgroup (see Kosaki and Yamagami) which are simultaneous semi-direct products. Subfactors are distinguished by looking at the dual action on the type II graphs. It is also possible to distinguish subfactors by investigating automorphisms appearing in the irreducible decomposition of the relevant sector (or bimodule).