It is known that GI is solvable in subexponential time n^polylog(n), which makes it unlikely to be NP-complete, unless the Exponential Time Hypothesis (ETH, see this market: https://manifold.markets/BoltonBailey/is-the-exponential-time-hypothesis?r=RmxvZmZpbm91) is wrong. If we believe in the ETH, GI could either be in P (see this market: https://manifold.markets/BoltonBailey/is-graph-isomorphism-in-p?r=RmxvZmZpbm91) or NP-intermediate:

https://en.wikipedia.org/wiki/NP-intermediate