ALT Subgroup lattice of the symmetric group S_4 and five Cayley graphs: four on Archimedean solids and one of the Nauru graph.

ALT Subgroup lattices of all five group of order 12, with their "towers of p-groups" colored, to illustrate the Sylow theorems.

ALT Subgroup lattices and Cayley graphs of both semidirect products of C_5 and C_4. On the left, the lattice of D_5 appears at the bottom (it's a subgroup), but it appears at the top of the one on the right (it's a quotient).

ALT The subgroup lattices of D_6 four times, highlighting three semidirect product decompositions, and one direct product decomposition.