Let $G$ be a cyclic group $G=\langle a\mid a^6\rangle $ and let $H=\langle a^2\rangle $. Is that true then there is one relation in $H$, $(a^2)^3=1$?

Question

Let $G$ be a cyclic group $G=\langle a\mid a^6\rangle $ and let $H=\langle a^2\rangle $.

My question is: Is that true then there is one relation in $H$, $(a^2)^3=1$?

Thank you