The question is :
In the group $(\mathbb Z_{2})^3$,find the number of subgroups isomorphic to $(\mathbb Z_{2})^2$.
I find difficulty in working out this question.Please help me.
EDIT :
I think it is possible in ${7\choose 2}$ ways.Because suppose we take $(0,0,0),(1,0,0),(0,1,0)$ as any three elements then the fourth element should be $(1,1,0)$.Isn't it?Hence we only have to take any two elements from the remaining $7$ by keeping identity element fixed, which is possible in only ${7 \choose 2}$ ways.Please verify whether it is correct or not.
Thank you in advance.