Consider the set $S =\{ a , b , c , d\}$ . Consider the following 4 partitions $π_1,π_2,π_3,π_4$ on
$S : π_1 =\{\overline{abcd}\} , π_2 =\{\overline{ab}, \overline{cd}\},$
$\quad\;\, π_3 = \{\overline{abc}, \overline{d}\}, π_4 =\{\bar{a}, \bar{b}, \bar{c}, \bar{d}\}$.
Let $\prec$ be the partial order on the set of partitions $S' = \{π_1,π_2,π_3,π_4\}$
defined as follows: $π_i \prec π_j$ if and only if $π_i$ refines $π_j$. The poset diagram for $(S',\prec)$ is: