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We study reductions of the Korteweg--de Vries equation corresponding tostationary equations for symmetries from the noncommutative subalgebra. Anequivalent system of $n$ second-order equations is obtained, which reduces tothe Painlev\'e equation P$_{34}$ for $n=1$. On the singular line $t=0$, asubclass of special solutions is described by a system of $n-1$ second-orderequations, equivalent to the P$_3$ equation for $n=2$. For these systems, weobtain the isomonodromic Lax pairs and B\"acklund transformations which formthe group ${\mathbb Z}^n_2\times{\mathbb Z}^n$.

Non-autonomous reductions of the KdV equation and multi-component analogs of the Painlev\'e equations P$_{34}$ and P$_3$