  We use Bott-Chern cohomology to measure the non-K\"ahlerianity of
6-dimensional nilmanifolds endowed with the invariant complex structures in M.
Ceballos, A. Otal, L. Ugarte, and R. Villacampa's classification, [Invariant
Complex Structures on 6-Nilmanifolds: Classification, Fr\"olicher Spectral
Sequence and Special Hermitian Metrics, J. Geom. Anal. (2014)]. We investigate
the existence of pluriclosed metric in connection with such a classification.
