The author admits to twisting the shape of the table to arbitrarily make it look like the table of elements, even though the only similarity is that both have some sense of 2-dimensionality.
The groups table is not "periodic" in any sense.
> I also considered the non-classical groups to be “less important” and so there are fewer rows of them to better match the look of the real periodic table. They also have larger orders so it makes sense to include fewer of them on the table.
> Since there are no “sporadic” elements, I had to decide what to do with the sporadic simple groups. These are groups that don’t fall into any of the other families. At one point I put them in the upper right corner with a jagged boundary like the non-metals. This made the table resemble the real periodic table, but it had more rows and less columns so it looked rather “thick”. Unfortunately, it didn’t make as much sense from an algebraic point of view, so I placed them where the lanthanides and actinides are found instead. This is slightly misleading, because if enough new elements were to be discovered there would be another row in that section. But you can’t have everything perfect. After all, there are an infinite number of simple groups, and only a finite number of elements.