  Solving functional equations given in \cite{nagy} for extensions of a group
$A$ by a weighted Steiner loop $S$ we obtain concrete description for all loops
with interesting weak associativity properties if the Steiner loop $S$ induces
only the trivial automorphism on $A$. We show that the restricted Fischer
groups and their geometry play an important role for loop extension with right
alternative property. Also the automorphism groups of these extensions as well
as the conditions for isomorphisms between two extensions are studied.
