We all know that if two subgroups $A \le G$ and $B \le G$ have coprime order $\gcd(|A|, |B|)=1$, then their intersection is trivial: $A \cap B=\{e\}$.
Does the converse of this statement remains true? I mean, is it true that if an intersection of two subgroups is trivial $A \cap B = \{e\}$, then their orders are coprime $\gcd(|A|, |B|)=1$?
I think that dihedral group $D_3$ may be a good counterexample here: subgroups of rotations and reflections have equal order, but do they intersect only by $\{e\}$? (seems wrong actually:))
Any other ideas?