Quartic half-arc-transitive graphs with large vertex stabilizers

A 12-arc-transitive graph is a vertex- and edge- but not arc-transitive graph. In all previously known constructions of quartic 12-arc-transitive graphs, vertex stabilizers are isomorphic to Z2,Z22 or to D8. In this article, for each positive integer m⩾1, an infinite family of quartic 12-arc-transitive graphs having vertex stabilizers isomorphic to Z2m is constructed.