Let \(G\) be a \(p\)-group, the `coclass' of \(G\) is defined as \(r=n-c\), where \(p^n\) is the order of \(G\) and \(c\) is the length of the lower central series of \(G\). There is a classification of finite \(p\)-groups according to their coclass: \textit{C. R. Leedham-Green} [J. Lond. Math. Soc. II, Ser. 50, No. 1, 49-67 (1994; Zbl 0822.20018)]. This is given by associating \(p\)-adic uniserial space groups. The main theorem of this paper is that for \(p=2\) and fixed coclass \(r\) there are finitely many isomorphism classes of cohomology rings of \(2\)-groups with coefficients in a fixed field of characteristic \(2\). More precisely: Theorem 5.1: Let \(k\) be a field of characteristic \(2\). For any natural number \(r\) there are only finitely many graded commutative \(k\)-algebras \(R\) with the property that \(R\cong H^*(G,k)\), where \(G\) is a \(2\)-group of coclass \(r\). The author proves this by analyzing various spectral sequences appearing in the calculation of such cohomology rings and counting the number of possible outcomes.