We need to prove that $D_{3} \oplus D_{4}$ is not isomorphic to $D_{24}$ .
The way in which I approach such type of questions is to count the number of elements of order $x$ in one group and then in the other group, and then conclude that they aren't equal and hence there can't be any isomorphism between them.
But this approach here doesn't look easy, with $D_{24}$ involved.
Could anyone suggest another way of solving this ?