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We provide a complete description of the presentations of the interval groupsrelated to quasi-Coxeter elements in finite Coxeter groups. In the simply lacedcases, we show that each interval group is the quotient of the Artin groupassociated with the corresponding Carter diagram by the normal closure of a setof twisted cycle commutators, one for each 4-cycle of the diagram. Ourtechniques also reprove an analogous result for the Artin groups of finiteCoxeter groups, which are interval groups corresponding to Coxeter elements. Wealso analyse the situation in the non-simply laced cases, where a new Garsidestructure is discovered.  Furthermore, we obtain a complete classification of whether the intervalgroup we consider is isomorphic or not to the related Artin group. Indeed,using methods of Tits, we prove that the interval groups of properquasi-Coxeter elements are not isomorphic to the Artin groups of the same type,in the case of $D_n$ when $n$ is even or in any of the exceptional cases. In[BHNR22], we show using different methods that this result holds for type $D_n$for all $n \geq 4$.

Interval groups related to finite Coxeter groups, Part II