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We describe the finite group actions, up to equivalence, which can act on the orbifold $\Sigma (2,2,2)$, and their quotient types. This is then used to consider actions on prism manifolds $M(b,d)$ which preserve a longitudinal fibering, but do not leave any Heegaard Klein bottle invariant. If $\varphi :G\to \text{Homeo}\left(M\right(b,d\left)\right)$ is such an action, we show that $M(b,d)=M(b,2)$ and $M(b,2)/\varphi$ fibers over a certain collection of 2-orbifolds with positive Euler characteristic which are covered by $\Sigma (2,2,2)$. For the standard actions, we compute the fundamental group of $M(b,2)/\varphi$ and indicate when...