  We investigate the interplay between altermagnetic spin-splitting and
nonsymmorphic symmetries using the space group no. 62 as a testbed. Studying
different magnetic orders by means of first-principles calculations, we find
that the altermagnetism (AM) is present in the C-type magnetic configuration
while it is absent for the G-type and A-type configurations due to different
magnetic space group types. The nonsymmorphic symmetries constrain the system
to a four-fold degeneracy at the border of the Brillouin zone with semi-Dirac
dispersion. In the case of large hybridization as for transition metal
pnictides, the interplay between AM and nonsymmorphic symmetries generates an
intricate network of several crossings and anticrossings that we describe in
terms of semi-Dirac points and glide symmetries. When we add the spin-orbit
coupling (SOC), we find a Neel-vector dependent spin-orbit splitting at the
time-reversal invariant momenta points since the magnetic space groups depend
on the Neel vector. The magnetic space group type-I produces antiferromagnetic
hourglass electrons that disappear in the type-III. When the Neel vector is
along x, we observe a glide-protected crossing that could generate a nodal-line
in the altermagnetic phase. The SOC splits the remaining band crossings and
band anticrossings producing a large anomalous Hall effect in all directions
excluding the Neel-vector direction
