Currently, space group is provided only with Hermann–Mauguin notation.

But HM notation is not useful when one wants to sort search results by the degree of symmetry.

It would be nice to have space group number column as well or a sorting option enabling “sort by symmetry degree”, not by alphabetical order of HM notation, without adding a new column.

What do you mean by sort by “degree of symmetry”?

If you mean the international number, I believe the international number is actually not well defined in this respect, while the numbers are grouped by crystal system so that (roughly speaking) symmetry increases as the number increases as we go from triclinic to cubic etc., within each crystal system I don’t think it’s meaningful to say that the numbers are sorted.