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Let $N^2_g$ be a non-orientable closed genus $g\geq 2$ surface. Is there a way to explicitly list the normal subgroups of $\pi_1(N^2_g)$ in terms of generators and relations? I am interested in understanding all possible normal coverings of $N^2_g$.

Thank you.

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    I assume that you are familiar with the fundamental group of non-orientable closed genus $g\ge 2$ surfaces $N_g^2$, namely $\pi_1(N_g^2,\ast)=\langle x_1,...,x_g|x_1^2\cdots x_g^2\rangle$. [This paper](http://www.math.uchicago.edu/~may/VIGRE/VIGRE2007/REUPapers/FINALFULL/Kreek2.pdf) tells you something about subgroups (not necessarily normal) of orientable genus $g$ surfaces. Maybe it is helpful to get a feeling for the general procedure.2015-10-05

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