  We recall the notion of Hopf quasigroups introduced previously. We construct
a bicrossproduct Hopf quasigroup $kM\bicross k(G)$ from every group $X$ with a
finite subgroup $G\subset X$ and IP quasigroup transversal $M\subset X$ subject
to certain conditions. We identify the octonions quasigroup $G_O$ as
transversal in an order 128 group $X$ with subgroup $Z_2^3$ and hence obtain a
Hopf quasigroup $kG_O\lcocross k(Z_2^3)$ as a particular case of our
construction.
