  We discuss a recent lattice study of charmonium-like mesons with
$J^{PC}=1^{++}$ and three quark contents $\bar cc\bar du$, $\bar cc(\bar uu +
\bar dd)$ and $\bar cc\bar ss$, where the latter two can mix with $\bar cc$. In
this quantum channel, the long known exotic candidate, X(3872), resides. This
simulation employs $N_f=2$, $m_\pi=266~$MeV and a large basis of $\bar cc$,
two-meson and diquark-antidiquark interpolating fields, with diquarks in both
anti-triplet and sextet color representations. It aims at the possible
signatures of four-quark exotic states. Along the way, we discuss the relations
between the diquark-antidiquark operators and the two-meson operators via the
Fierz transformations.
