Subgroup Lattice of Z/4Z x Z/2Z x Z/2Z

The 3D object shown below on the left is a lattice describing the subgroups of Z/4Z x Z/2Z x Z/2Z, ordered by inclusion. The picture on the right is the Hasse diagram describing the inclusion relations of the subsets of a multiset of type (2,1,1). When the 3D picture is oriented correctly, the pictures suggest an order preserving surjection from the lattice of subgroups onto the multiset lattice.

Drag your mouse on the left hand picture to change orientation.
Hasse diagram of (2,1,1)
More information about these sets can be found on Lynne Butler's undergraduate research page. The Java 3D viewer was written by Daeron Meyer at the Geometry Center.
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