Classifying 2-groups by coclass

Now that the conjectures of Leedham-Green and Newman have been proved, we probe deeper into the classification of $p$-groups using coclass. We determine the pro-$2$-groups of coclass at most 3 and use these to classify the 2-groups of coclass at most 3 into families. Using extensive computational evidence, we make some detailed conjectures about the structure of these families. We also conjecture that the 2-groups of arbitrary fixed coclass exhibit similar behaviour.