jmc

If Henry is in the group of 4, there are $\left(\genfrac{}{}{0ex}{}{11}{3}\right)=165$ ways to choose the other people in the group of 4. Then there are $\left(\genfrac{}{}{0ex}{}{8}{3}\right)=56$ ways to choose the group of 3, and the group of 5 is made up of the remaining people. The total number of valid ways to divide the people into groups is $165\cdot 56=\boxed{9240}$.