Brand architecture should have five dimensions: brand portfolio, portfolio roles product-market context roles, the portfolio strukcture, and portfolio graphics. While we know five dimensions there are six objectives to be followed if the designing the brand architecture is to achieve a an effective and powerful brand impact (Aaker and Joachimsthaler, 2000, p. 134-135). And the powerful system of the brand architecture is the prerequisite in the development of the corporate identity.
Figure source: Aaker and Joachimsthaler, 2000, p. 135
Source: Aaker, David A. and Joachimsthaler, Erich. 2000. Brand Leadership. 2000. The Free Press. 350 p.