  The normaliser problem takes as input subgroups $G$ and $H$ of the symmetric
group $S_n$, and asks one to compute $N_G(H)$. The fastest known algorithm for
this problem is simply exponential, whilst more efficient algorithms are known
for restricted classes of groups. In this paper, we will focus on groups with
many orbits. We give a new algorithm for the normaliser problem for these
groups that performs many orders of magnitude faster than previous
implementations in GAP. We also prove that the normaliser problem for the
special case $G=S_n$ is at least as hard as computing the group of monomial
automorphisms of a linear code over any field of fixed prime order.
