Connection between Lorentz group and rotation group

The rotation group can be thought of as $3\times 3$ matrices $R$ that satisfies $I=R^{T}IR$, while the Lorentz group is $\eta ={\mathrm{\Lambda }}^T\eta \mathrm{\Lambda }$, where $I$ is the Euclidean metric and $\eta$ is Lorentzian^[1].

_{[1] Carroll Sean (2003). Spacetime and Geometry - an Introduction to General Relativity}