\chapcontents {1}{Preface}{3} \chapcontents {2}{Introduction to GrpConst}{4} \chapcontents {3}{Construction of All Groups}{5} \chapcontents {4}{The Frattini Extension Method}{6} \seccontents {4.1}{The Main Frattini Extension Function} {6} \seccontents {4.2}{The Construction of Frattini Free Groups} {7} \seccontents {4.3}{The Determination of Frattini Extensions} {8} \seccontents {4.4}{Verifying non-isomorphism} {9} \chapcontents {5}{The Cyclic Split Extension Method}{10} \seccontents {5.1}{The Main Function} {10} \seccontents {5.2}{The Underlying Functions} {11} \chapcontents {6}{The Upwards Extension Method}{12} \chapcontents {7}{Examples with Runtimes}{14} \chapcontents {}{Bibliography}{16}