Triops, and married his brother (i.e. her uncle) Alöeus. Later, however, she fell in love with Poseidon and bore him two giants, Otus and Ephialtes. In her association with Poseidon, she used to sit by the sea and wash its waters into her lap to achieve impregnation (Poseidon, of course, was the great god of the sea and waters).
This, and the fact that she bore two giants, suggest an interpretation of her name as not so much 'strong ruler', from iphi, 'mightily' and medeon, 'ruler', which would be the traditional reading, as 'bearing mightily', from iphi and medea, 'genitals'. 'She who strengthens the genitals' is Robert Graves' rendering. Compare Ganymede.