  We determine the intrinsic shapes and orientations of 27,450 type I and II
active galactic nucleus (AGN) galaxies in the spectroscopic sample of the SDSS
DR7, by studying the distribution of projected axis ratios of AGN hosts. Our
aim is to study possible alignments between the AGN and host galaxy systems
(e.g. the accretion disc and the galaxy angular momentum) and the effect of
dust obscuration geometry on the AGN type. We define control samples of non-AGN
galaxies that mimic the morphology, colour, luminosity and concentration
distributions of the AGN population, taking into account the effects of dust
extinction and reddening. Assuming that AGN galaxies have the same underlying
three-dimensional shape distribution as their corresponding control samples, we
find that the spiral and elliptical type I AGN populations are strongly skewed
toward face-on galaxies, while ellipticals and spirals type II AGN are skewed
toward edge-on orientations. These findings rule out random orientations for
AGN hosts at high confidence for type I spirals (delta chi^2~230) and type II
ellipticals (delta chi^2~15), while the signal for type I ellipticals and type
II spirals is weaker (delta chi^2~3 and delta chi^2~6, respectively). We obtain
a much stronger tendency for the type II spirals to be edge-on when just high
[OIII] equivalent width (EW) AGN are considered, suggesting that >20% of low
[OIII] EW edge-on type II AGN may be missing from the optical sample. Galactic
dust absorption of the broad-line region alone cannot explain the observed
inclination angle and projected axis ratio distributions of type I and II
Seyfert types, implying that obscuration by a small-scale circumnuclear torus
is necessary. These results favour a scenario in which the angular momentum of
the material which feeds the black hole retains a memory of its original gas
source at least to some small, non-negligible degree.
