We obtain defining equations of the smooth equivariant compactification of the Grassmannian of the complex associative 3-planes in \(\mathbb C^7\), which is the parametrizing variety of all quaternionic subalgebras of the algebra of complex octonions \(\mathbb O\cong \mathbb C^8\). By studying the torus fixed points, we compute the Poincaré polynomial of the compactification.