I tried getting $n_{2}$ and $n_{7}$ , denote the number of Sylow-2-Subgroups and Sylow-7-Subgroups respectively.
I got two cases for $n_{2} = 1 , 7 $ and for $n_{7} = 1 , 8$ , i noticed that if $n_{2} = 1$ and $n_{7}= 1$ ,then we are done since they are unique subgroups and hence will be normal in $G$.
Next how to proceed with the cases of $n_{2} = 7$ and $n_7 = 8$.
Please help?