I have a question which is: find the composition factors of a group of order $48$. But I can't see how I can do this.
If I choose my group to be $C_{48}$ then it has composition series : $\{1\}\triangleleft C_2 \triangleleft C_4 \triangleleft C_8 \triangleleft C_{16} \triangleleft C_{48}$ So the composition factors are $C_3$ and four $C_2$.
But then if I choose a different group from Sylow theory I have that there is either a normal subgroup of order $16$ or $8$. So if it is not $16$, it is $8$ so call it $N$, then we have a subnormal series with $\{1\} \triangleleft N \triangleleft G$ where any refinment will be to the left of $N$ so we have a composition factor of size 6?
Have I done something wrong?
Thanks for any help