Geodesic
Subgroup Lattices for Crystallographic Groups
Many of the properties of the two-dimensional crystallographic groups may be discovered by looking at the subgroup relationships between the groups. Utilizing subgroup lattices, this paper investigates patterns that occur among the groups, their planar lattices and point groups. This includes a description on how the various groups sit inside one another as subgroups and also investigates techniques whereby removing symmetry from one of the crystallographic groups produces another group
Classification : 20H15 
@article{VM_2002_4_4_a3,
     author = {Raymond F. Tennant},
     title = {Subgroup {Lattices} for {Crystallographic} {Groups}},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_2002_4_4_a3/}
}
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Raymond F. Tennant. Subgroup Lattices for Crystallographic Groups. Visual Mathematics, Tome 4 (2002) no. 4. http://geodesic.mathdoc.fr/item/VM_2002_4_4_a3/