Does lepton family number always have to be conserved?

So for example, is the following reaction possible?:

$$\mu^- \rightarrow e^- + \gamma$$

In the textbook it says this is possible, as it conserves the lepton number. However, the lepton flavour is not conserved, as no muon neutrino is produced, and no antielectron neutrino is produced as well. Shouldn’t this not be possible? Or is family lepton number conservation not required for reactions?