No. of inequivalent sudokus

[N. J. A. Sloane]

I'm sending this to both the math fun and seq fan lists,
becuse even though it is about a sequence, most of the sudoku
discussions i've seen have been on the former list.

The number of (completed) n^2 X n^2 sudokus is:
%I A107739
%S A107739 1,1,288,6670903752021072936960
%N A107739 Number of (completed) sudokus of size n^2 X n^2.
based on 
%H A107739 Bertram Felgenhauer and Frazer Jarvis,
http://www.shef.ac.uk/~pm1afj/sudoku/
There are 6670903752021072936960 Sudoku grids


Ed Russell and Frazer Jarvis also compute the number of inequivalent 9x9's,
see
"There are 5472730538 essentially different Sudoku grids"
http://www.shef.ac.uk/~pm1afj/sudoku/sudgroup.html

allowing (i quote)

    Relabelling entries;
    Reflection;
    Rotation;
    Permutation of blocks of columns 1-3, 4-6 and 7-9;
    Permutation of blocks of rows 1-3, 4-6 and 7-9;
    Permutation of columns 1-3;
    Permutation of rows 1-3;
    Permutation of columns 4-6;
    Permutation of rows 4-6;
    Permutation of columns 7-9;
    Permutation of rows 7-9.

So there's a new sequence here:

0    1    2      3
1    1    x   5472730538

where x is some small number!  My question is, what is x?
Using analogues of the above transformations, how many
inequivalent 4 X 4 grids are there?

Hugo van der Sanden sent me an upper bound x <= 6, since any 4X4 
grid is equivalent to one of:

1234 1234 1234 1234 1234 1234
3412 3412 3421 4312 4321 4321
2143 2341 2143 2143 2143 2413
4321 4123 4312 3421 3412 3142

but this can surely be reduced. So is x 1, 2 or 3?

NJAS