  We determine the exact value of the $\eta$-constant and the multiwise
Davenport constants for finite abelian groups of rank three having the form $G
\simeq C_2 \oplus C_{n_2} \oplus C_{n_3}$ with $2 \mid n_2 \mid n_3$. Moreover,
we determine the Erd\H{o}s-Ginzburg-Ziv constant of these groups under the
assumption that $n_2/2$ has Property D or $n_2 = n_3$.
