In , Greenberg showed that n <= 6t(3) so that mu - nt <= 6t(4) for a normal subgroup N of level n and index mu having t parabolic classes in the modular group Gamma. Accola, , improved these to n <= 6t(2) always and n <= t(2) if Gamma/N is not abelian. Newman, , obtained another generalisation of these results. Hecke groups are generalisations of the modular group. We particularly deal with one of the most important cases, q = 6.