# Normal subgroups of the semidihedral group of order 16?

What are the normal subgroups of the semidihedral group of order 16? For such a fundamental result, there doesn't seem to be a reference to this online...

The semidihedral group of order 16 is given by $\langle \sigma, \tau\rangle$, where $\sigma^8 = \tau^2 = e$ and $\sigma\tau = \tau\sigma^3$.

• Are you sure you mean $\sigma^3$? – GPerez Jun 3 '15 at 11:20

There are 6 normal subgroups, namely, the trivial subgroup, $\langle\sigma^4\rangle$, $\langle\sigma^4, \tau\rangle$, $\langle\sigma^2\rangle$, $\langle\sigma^2, \tau\rangle$, and $\langle\sigma\rangle$.