@BalarkaSen Another quick verification, $|G|=99=3^2\times 11$ gives us $n_{3}=1,n_{11}=1$ which gives us trivial intersection of normal $p,q$ sylow subgroups, and $P\cong \Bbb Z/11\Bbb Z$ $Q\cong \Bbb Z/9\Bbb Z$ or $\Bbb Z/3\Bbb Z\times \Bbb Z/3\Bbb Z$ and this gives way to two isomorphism classes for $G$, one cyclic, one non-cyclic:

$$\Bbb Z/11\Bbb Z \times \Bbb Z/ 9 \Bbb Z\cong \Bbb Z/99\Bbb Z, \quad \Bbb Z/3\Bbb Z \times \Bbb Z/3\Bbb Z \times \Bbb Z/11\Bbb Z\cong \Bbb Z/3 \Bbb Z \times \Bbb Z/33\Bbb Z$$