Wyckoff Positions and Standard Cell

We process the C2DB database with `spglib.get_layergroup`. Positions of atoms are recorded as `std_positions` in `spglib`.
And things went wrong for some materials, such as https://c2db.fysik.dtu.dk/material/2AgNaTe-1 with layer group No. 64.
For Wyckoff position `2a`, the coordinates given in https://www.cryst.ehu.es/ are `(3/4, 1/4, 0)` and `(1/4, 3/4, 0)`.
However, the `2a` Wyckoff positions in `spglib` are `(1/2, 0, 0)` and `(0, 1/2, 0)`.

We can check the layer group operations of `spglib`.
The operations on input cell are stored as `rotations` and `translations`.
And the transformation between input cell and standard cell is stored as `transformation_matrix` and `origin_shift`.
So we can calculate the operations on standard cell, they are listed as following:
`(x, y, z) (-x, y, z) (x, -y, z) (-x, -y, z) (y, x, z) (-y, x, z) (y, -x, z) (-y, -x, z) (x+1/2, -y+1/2, -z) (-y+1/2, -x+1/2, -z) (-x+1/2, y+1/2, -z) (y+1/2, x+1/2, -z) (-x+1/2, -y+1/2, -z) (y+1/2, -x+1/2, -z) (x+1/2, y+1/2, -z) (-y+1/2, x+1/2, -z)`.
This is different from the operations recorded in https://www.cryst.ehu.es/, which is
`(x,y,z) (-x+1/2,-y+1/2,z) (-y+1/2,x,z) (y,-x+1/2,z) (-x,y+1/2,-z) (x+1/2,-y,-z) (y+1/2,x+1/2,-z) (-y,-x,-z) (-x,-y,-z) (x+1/2,y+1/2,-z) (y+1/2,-x,-z) (-y,x+1/2,-z) (x,-y+1/2,z) (-x+1/2,y,z) (-y+1/2,-x+1/2,z) (y,x,z)`.

These two *groups* of operations may be isomorphic to each other, i.e., they are just expressed in two different coordinate systems.
But the problem is how to check they are isomorphic, and find the isomorphism (the transformation between the two set of coordinate systems)?
Because `CrystalFormer` works under the coordinate system given by https://www.cryst.ehu.es/, so we need to perform the transformation so that `CrystalFormer` *recognizes* the output of `spglib`.