Let $G$ be a locally compact Hausdorff group. Denote its Bohr compactification with $bG$.

Despite group structure, $G$ has several (Hausdorff) compactifications that,in a sense, the smallest one is the one-point compactification, and the largest one is the Stone-Cech compactification.

Is $bG$ is isomorphic to one of (topological) compactifications of $G$ as a topological space? In the case of positive answer, to which one? I don't know answer even in the case of $G=\mathbb{R}$.