Relationship between orders of $Ng\in \frac{G}{N}$ and $q\in Q$ if $G=N\cdot Q$.

Question

Let $G=N\cdot Q$ be a finite extension. What is the relationship between the orders of a coset $Ng\in \frac{G}{N}$ and an element $q\in Q$?

I know that by the natural homomorphism

$$f:G\longrightarrow \frac{G}{N},$$

the group $Q$ can be identified with the quotient group $\frac{G}{N}$.

So is it correct to say that for a lifting $g$ of $q$ in $G$ that the coset $Ng$ can be identified with $q$ and hence $o(Ng)=o(q)$?