From the given pie chart, the total percentage of students placed across different branches is:
\[
28\% + 19\% + 15\% + 17\% + 13\% = 92\%.
\]
Thus, the total number of students placed is 92\% of the total student population. Given that the total number of students is 236, we calculate the number of students placed as follows:
\[
\frac{92}{100} \times 236 = 217.
\]
Hence, the number of students placed is 217.