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We consider the (extended) metaplectic representation of the semidirectproduct $\mathcal{G}={\mathbb H}^d\rtimes Sp(d,{\mathbb R})$ between theHeisenberg group and the symplectic group. Subgroups $H=\Sigma \rtimes D$, with$\Sigma$ being a $d\times d$ symmetric matrix and $D$ a closed subgroup of$GL(d,{\mathbb R})$, are our main concern. We shall give a general setting forthe reproducibility of such groups which include and assemble the ones for thesingle examples treated in [5]. As a byproduct, the extended metaplecticrepresentation restricted to some classes of such subgroups is either theSchr\"odinger representation of ${\mathbb R}^{2d}$ or the waveletrepresentation of ${\mathbb R}^d\rtimes D$, with $D$ closed subgroup of$GL(d,{\mathbb R})$. Finally, we shall provide new examples of reproducinggroups of the type $H=\Sigma\rtimes D$, in dimension $d=2$.

Triangular Subgroups of $Sp(d,{\mathbb R})$ and Reproducing Formulae