The eight trigrams are set out in two standard circular orders, and they are not variants of one diagram. The Earlier Heaven arrangement, attributed to Fuxi, is symmetrical, with every trigram facing its exact opposite, and in it Qian stands in the south with Kun opposite in the north. The Later Heaven arrangement, attributed to King Wen, is the order used in nearly all applied work, from the classical commentaries to the compass schools of feng shui, and in it Qian sits in the northwest.
Nothing about the trigram changes between them. What changes is the question the diagram answers. Earlier Heaven describes an ideal and static cosmos held in balance. Later Heaven describes the world in motion, ordered by the turning of the seasons and the phases, and its positions follow that cycle rather than a symmetry.
In the Later Heaven order Qian belongs to the phase Metal, which it shares with Dui, and to the turn from late autumn into winter. The Shuogua, the Discussion of the Trigrams among the Ten Wings, supplies the rest of the standard set: among animals Qian is the horse, among the parts of the body the head, and in the family scheme it is the father, the trigram of unmixed yang from which each of the three sons takes its single yang line.
Read the two arrangements as two maps of the same eight things and the system holds together. Read them as one diagram and the directions contradict each other on the first comparison.
Sources Fathoming the Cosmos and Ordering the World: The Yijing (I Ching, or Classic of Changes) and Its Evolution in ChinaRichard J. Smith with The I Ching, or Book of ChangesRichard Wilhelm (trans.); Cary F. Baynes (English trans.), The Five "Confucian" ClassicsMichael Nylan