Wada's conjecture on class groups of imaginary quadratic fields

Let $K=\mathbb{Q}(\mathbb{\sqrt{-D}})$ be an imaginary quadratic field, where $D>1$ is square-free, and write its class group as a direct product of cyclic groups. For integers $h_1,\ldots,h_t$, denote this group by $[h_1,\ldots,h_t]$. If the field has at least three ramified rational primes, write the relevant even factors in terms of powers of $2$. Wada's conjecture. All the class groups of imaginary quadratic fields are either cyclic or of the type $(h_1,h_2,2^{r_1},2^{r_2},\ldots,2^{r_k})$. The paper claims that its family of fields provides a counterexample to Wada's conjecture, so the conjecture is refuted.