The slice filtration focuses on producing certain spectra, called slices, from a genuine $G$-spectrum $X$ over a finite group $G$. There are several constructions which inflate a $G/N$-spectrum $X$ to a $G$-spectrum, which generally do not coincide. We will examine three such constructions, when they coincide, and how this relates to the slices of $\Sigma^n H\mathbb{Z}$ over $Q_8$.