  The paper is devoted to projective Clifford groups of quantum $N$-dimensional
systems. Clearly, Clifford gates allow only the simplest quantum computations
which can be simulated on a classical computer (Gottesmann-Knill theorem).
However, it may serve as a cornerstone of full quantum computation. As to its
group structure it is well-known that -- in $N$-dimensional quantum mechanics
-- the Clifford group is a natural semidirect product provided the dimension
$N$ is an odd number. For even $N$ special results on the Clifford groups are
scattered in the mathematical literature, but they don't concern the semidirect
structure. Using appropriate group presentation of $SL(2,Z_N)$ it is proved
that for even $N$ projective Clifford groups are not natural semidirect
products if and only if $N$ is divisible by four.
