The imperial line breaks at least twice, even if you don’t count the mythological emperors and assume that emperors are in fact the trueborn sons of the previous emperors that they’re claimed to be. At one point the line schisms in pope/antipope style and iirc the following line descends from the one with the weaker claim.

In any case the emperor has for most of this time been a ceremonial religious front for the actual power in the realm, which has variously been the head of dominant clans, a parliament, the two bakufus (three, if you count the system established between the two world wars where the military subverted the parliamentary system that ruled in name of the emperor), and for one interesting stretch the retired ex-emperors.