I am reading Dummit and Foote Section 4.4 on Automorphisms.

In the second papragraph of the secion Dummit and Foote write:

"Notice that automorphisms of a group G are, in particular, permutations of the set G so Aut(G) is a subgroup of

"

Intuitively it seems to me, at first reflection, at least, that any permututation of G would be an automorphism of G, but based on D&F's statement this is not the case

Can anyone with more experience of algebra explain at a broad intuitive level why this is not the case?

Peter