Several generalized notions of normality exist in the literature. In this paper, some variants of normality which lies between normal and $k$-normal (or mildly normal) spaces are considered. Interrelation among these variants of normality is established and examples are provided in their support. Some new decompositions of normality is obtained in terms of seminormal spaces and $\beta$-normal spaces. A weaker version of seminormal spaces is introduced which provides a factorization of normality in terms of $\pi$-normality.