Threefold extremal contractions of type (IIA). I

Let $(X,C)$ be a germ of a threefold $X$ with terminal singularities along an irreducible reduced complete curve $C$ with a contraction $f\colon(X,C)\to(Z,o)$ such that $C=f^{-1}(o)_{\mathrm{red}}$ and $-K_X$ is ample. Assume that $(X,C)$ contains a point of type $(\mathrm{IIA})$ and that a general member $H\in|\mathscr O_X|$ containing $C$ is normal. We classify such germs in terms of $H$.