A uniform lamina \(A B C D\) consists of two isosceles triangles \(A B D\) and \(B C D\). The diagonals of \(A B C D\) meet at the point \(O\). The length of \(A O\) is \(3 a\), the length of \(O C\) is \(6 a\) and the length of \(B D\) is \(16 a\) (see diagram).

Find the distance of the centre of mass of the lamina from \(D B\).