### A class of Bol loops with a subgroup of index two

Let $G$ be a finite group and ${C}_{2}$ the cyclic group of order $2$. Consider the $8$ multiplicative operations $(x,y)\mapsto {\left({x}^{i}{y}^{j}\right)}^{k}$, where $i$, $j$, $k\in \{-1,\phantom{\rule{0.166667em}{0ex}}1\}$. Define a new multiplication on $G\times {C}_{2}$ by assigning one of the above $8$ multiplications to each quarter $(G\times \{i\left\}\right)\times (G\times \{j\left\}\right)$, for $i,j\in {C}_{2}$. We describe all situations in which the resulting quasigroup is a Bol loop. This paper also corrects an error in P. Vojtěchovsk’y: On the uniqueness of loops $M(G,2)$.