How many symmetry elements are there for a cubic structure or a crystal ? 

Explanation

There are 3 types of symmetry elements.
They are: (a) centre of symmetry, (b) axis of symmetry and (c) plane of symmetry. A cube has 1 centre of symmetry. A cube has 3 axis of four fold symmetry, 4 axis of three fold symmetry and 6 axis of two fold symmetry.
A cube has 3 rectangular planes of symmetry and 6 diagonal planes of symmetry. The total number of symmetry elements of a cube `= 1+ (3+4+6) +(3+6) = 23.`