  We present a conformal isometry for static extremal black hole solutions in
all four-dimensional Einstein-Maxwell-scalar theories with electromagnetic
duality groups `of type $E_7$'. This includes, but is not limited to, all
supergravity theories with $\mathcal{N}>2$ supersymmetry and all
$\mathcal{N}=2$ supergravity theories with symmetric scalar manifolds. The
conformal isometry is valid for arbitrary electromagnetic charge configurations
and relies crucially on the notion of Freudenthal duality.
