Let $G$ be a finite group. Consider the lattice $$L=\{ G/N:\text{$ N $ is a normal subgroup of $G $}\},$$ where $G/N \leq G/K$ if and only if $K\leq N$. The lattice operations ∧ and ∨ on quotient groups $G/N, G/K$ are just $G/(NK)$ and $G/(N \cap K)$ respectively.

Is there a lattice $L^{1}$ ordered by inclusion and isomorphic to $L$ such that the cardinality of the corresponding elements of $L$ and $L^{1}$ are equal?