Matrices of 3-iet preserving morphisms

We study matrices of morphisms preserving the family of words coding 3-interval exchange transformations. It is well known that matrices of morphisms preserving Sturmian words (i.e. words coding 2-interval exchange transformations with the maximal possible factor complexity) form the monoid , where .We prove that in the case of exchange of three intervals, the matrices preserving words coding these transformations and having the maximal possible subword complexity belong to the monoid , where .