A semitopological group is a group with a topology under which the operation is separately continuous. The authors characterize when such a group embeds into a product of strongly metrizable semitopological groups. The characterization reads: if and only if the group is completely \(\omega\)-balanced and satisfies \(Ir(G)\leq\omega\). The former property stipulates that for every member~\(U\) of the neighbourhood filter \(\mathcal{N}(e)\) of the identity the cover \(\{Ux:x\in G\}\) has an open refinement~\(\mathcal{V}\) that is \(\sigma\)-star-countable, is such that for every~\(x\) there is a \(V\in\mathcal{V}\) with \(x\in V\subseteq Ux\), and is also such that there is a countable subfamily \(\mathcal{W}\) of~\(\mathcal{N}(e)\) with the property that whenever \(V\in\mathcal{V}\) and \(x\in V\) there is \(W\in\mathcal{W}\) with \(xW\subseteq V\). The invariant \(Ir\) (index of regularity) is the smallest cardinal~\(\kappa\) such that for every \(U\in\mathcal{N}(e)\) there is \(\mathcal{W}\subseteq\mathcal{N}(e)\) of cardinality at most~\(\kappa\) with \(\bigcap_{W\in\mathcal{W}}VW^{-1}\subseteq U\) for some \(V\in\mathcal{N}(e)\).