A note on meta and para-$\mathfrak{N}\mathfrak{i}\mathfrak{l}$-Hamiltonian groups_

Let $\mathfrak{N}\mathfrak{i}\mathfrak{l}$ be the class of nilpotent groups. This article explores the finiteness of meta and para-$\mathfrak{N}\mathfrak{i}\mathfrak{l}$-Hamiltonian groups or their derived subgroups when these groups contain a soluble subgroup of finite index or a non-nilpotent (or insoluble) subgroup of finite order respectively.