Let $y ^ { 2 } = 12 x$ be the parabola and $S$ be its focus. Let PQ be a focal chord of the parabola such that $( \mathrm { SP } ) ( \mathrm { SQ } ) = \frac { 147 } { 4 }$. Let C be the circle described taking PQ as a diameter. If the equation of a circle $C$ is $64 x ^ { 2 } + 64 y ^ { 2 } - \alpha x - 64 \sqrt { 3 } y = \beta$, then $\beta - \alpha$ is equal to $\_\_\_\_$ .