If $G$ is a group and $|G| = 2018$, then how many subgroup of $G$, let's say $H$, such that $|H| = 12$?
I don't quick and theorized ways to determine how many subgroup if the cardinality given. Lagrange Theorem connects factor group, not in this case. Do you have any idea? Regards.
Lagrange's Theorem states that if $H$ is a subgroup of a finite group $G$, then the order $|H|$ divides $|G|$. Since $12$ does not divide $2018$, there cannot be any subgroup of order $12$, i.e. the answer is $0$.