Let $p>2$ be prime. By the classification of quadratic forms, there are $8$ pairwise non-equivalent isotropic orthogonal groups in $4$ variables. Is there a concrete classification of orthogonal groups of these groups? Could they be isomorphism? The analogous question for $3$ variables has been asked and answered in a previous question of mine ( $p$-adic analogues of $\mathrm{SO}(3)$ ) but the method used there does not apply to forms with $4$ variables.