Let \(G\) be a group of order \(168.\)
Then, \(G\) may or may not be simple.
For example, \(G = \mathbb{Z}/168\mathbb{Z}\) is an example of a non-simple group of order \(168.\) This can be easily verified by considering the subgroup \(H = \{0, 84\} \le G.\) This is clearly normal as \(G\) is abelian.
On the other hand, see this paper for the existence as well as uniqueness of a simple group of order \(168.\)