  Let k be an arbitrary field of characteristic zero. In this paper we study
quotients of k-rational conic bundles over projective line by finite groups of
automorphisms. We construct smooth minimal models for such quotients. We show
that any quotient is birationally equivalent to a quotient of other k-rational
conic bundle cyclic group of order $2^k$, dihedral group of order $2^k$,
alternating group of degree $4$, symmetric group of degree $4$ or alternating
group of degree $5$ effectively acting on the base of conic bundle. Also we
construct infinitely many examples of such quotients which are not
k-birationally equivalent to each other.
