Strongly solid group factors which are not interpolated free group factors

We give examples of non-amenable ICC groups $\mathrm{\Gamma }$ with the Haagerup property, weakly amenable with constant ${\mathrm{\Lambda }}_{\text{cb}}(\mathrm{\Gamma })=1$, for which we show that the associated $\mathrm{I}{\mathrm{I}}_1$ factors $L(\mathrm{\Gamma })$ are strongly solid, i.e. the normalizer of any diffuse amenable subalgebra $P\subset L(\mathrm{\Gamma })$ generates an amenable von Neumann algebra. Nevertheless, for these examples of groups $\mathrm{\Gamma }$, $L(\mathrm{\Gamma })$ is not isomorphic to any interpolated free group factor $L({\text{F}}_t)$, for $1<t\le \mathrm{\infty }$.