Spin of photons/gamma ray transitions

[freeman2]

When I look at a nuclear level scheme, there are many gamma ray transitions from energy levels of say, spin 4 to spin 2. However, my understanding was that photons carry spin 1, and so conservation of angular momentum would say that you can only change the spin of a level by 1. What am I missing here? Can photons carry any integer spin, eg 1,2,3...?

 

[Vanadium 50]

The photon can be emitted with orbital angular momentum relative to the emitting nucleus.