ERD for my simple db design:

I want to order children based on their parent's last name. I am trying to use the following query:

SELECT * FROM children WHERE parent_id IN (SELECT parent_id FROM parent ORDER BY lastName ASC);

SELECT parent_id FROM parent ORDER BY lastName ASC returns the parent_ids in the order of the parent's last names (this is the intended behavior). The ordering of parent_ids according to their last names in ascending order is 154,156,155,157

However, when used as a subquery, the ordering is apparently not used correctly. The results are:

As you can see the results are ordered in ascending order of parent_id (not of the child's respective parent's last name).

Is there a way to correctly structure this query without changing my design?

Thank you.