  A graph $\Gamma$ is basic if Aut$\Gamma$ has no normal subgroup $N\ne1$ such
that $\Gamma$ is a normal cover of the normal quotient graph $\Gamma_N$. In
this paper, we completely determine the basic normal quotient graphs of all
connected 7-valent symmetric graphs of order $2pq^n$ with $p < q$ odd primes,
which consist of an infinite family of dihedrants of order $2p$ with
$p\equiv1$(mod 7), and 6 specific graphs with order at most 310. As a
consequence, it shows that, for any given positive integer n, there are only
finitely many connected 2-arc-transitive 7-valent graphs of order $2pq^n$ with
$7\ne p<q$ primes, partially generalizing Theorem 1 of Conder, Li and Potocnik
[On the orders of arc-transitive graphs, J. Algebra 421 (2015), 167-186].
