Probably, the number of groups of order $18,480$ can only be determined with GAP. But I may be wrong, so the question should not be understood to be purely computational. A better lower bound than my mentioned $1,005$ or a good upper bound would also be welcome.
I tried to determine the number of groups of order $18,480$ with GAP.
My GAP version once again failed because of a memory overflow. The final output :
#I Iso: test isomorphism on groups of size 18480
gap: cannot extend the workspace any more!
gap: Press <Enter> to end program
What is $gnu(18,480)$ ? Please approve with ForAll(x,IsGroup) , that the groups are actually non-isomorphic.
What is the best upper bound, which can be determined without great effort ?
The calculation for $9,240$ worked well and gives a lower bound for the desired value.
9240:779:[ [ 2, 3 ], [ 3, 1 ], [ 5, 1 ], [ 7, 1 ], [ 11, 1 ] ]:true
A better lower bound is $gnu(1,680)=1,005$.
Since the factorization of $\ \ 18,480=2^4\cdot3\cdot5\cdot7\cdot11\ \ $ has no large prime-power, there might be a method to determine the number of groups even without electronic help. Is someone has an idea, he/she is invited to show the method and the result.
$5397$ isomorphism classes of groups. About 5 hours, under 1 GB in (development version of) GAP.