  We study invariant random subgroups (IRSs) of semidirect products $G = A
\rtimes \Gamma$. In particular, we characterize all IRSs of parabolic subgroups
of $\mathrm{SL}_d(\mathbb{R})$, and show that all ergodic IRSs of $\mathbb{R}^d
\rtimes \mathrm{SL}_d(\mathbb{R})$ are either of the form $\mathbb{R}^d \rtimes
K$ for some IRS of $\mathrm{SL}_d(\mathbb{R})$, or are induced from IRSs of
$\Lambda \rtimes \mathrm{SL}(\Lambda)$, where $\Lambda < \mathbb{R}^d$ is a
lattice.
