If $K\triangleleft G$ so the subgroups from $G/K$ are quotient groups $H/K$ with $K<H<G$ and $H/K \triangleleft G/K$ is equivalent to $H \triangleleft G$.
I didn't understand "are quotient groups $H/K$". Does it mean that the subgroups from $G/K$ are given by $H/K$? Has this proposition been badly written?