There are three different types of symmetries which are possible in a crystal. A crystal may have different numbers of each kind of symmetry. The total number of planes, axes and centre of symmetries possessed by a crystal is termed an element of symmetry of the crystal.
To explain this term further, consider the elements of symmetry possessed by a cubic crystal, such as NaCl crystal. A cubic crystal, such as NaCl crystal, contains a cubic crystal. This crystal has a total of 23 elements of symmetry; as will the discussion is given below. These elements of symmetry are,
One rectangular plane of symmetry is shown in fig (a). there will be two more such planes, each at right angles to the plane. Thus, there are three rectangular planes of symmetry in all.
Diagonal planes of symmetry
One plane passes diagonally through the cube, as shown in fig (b). there can be a total of 6 such planes passing diagonally through the cube, as a bit of reflection will show.
Axes of four-fold symmetry
One of the four-fold axes is shown in fig c. There can be a total of 3 such four-fold axes at right angles to one another.
Axes of three-fold symmetry
One such axis passing through opposite corners is shown in fig d. there can be a total of four three-fold axes.
Axes of two-fold symmetry
Fig (e) shows one such axis emerging from opposite edges. There are, evidently, six such axes of two-fold symmetry.
Centre of symmetry
There is only one center of symmetry  lying at the center of the cube, as shown in fig f. the number of symmetry elements of various types in the cubic crystal is;
Planes of symmetry = 3 + 6 = 9 elements
Axes of symmetry = 3 + 4 + 6 =13 elements
Centre of symmetry = 1
Total number of symmetry elements = 23
