One detail that always struck me: none of the soldiers are looking at their victims. They're looking down, as if Goya is showing that they know what they're doing is wrong, but can't bear to see the consequences of their actions. War makes victims of us all.
Or perhaps they are looking at the iron sights, caring more if they are aiming properly and carry out the orders, ignoring the humans standing behind it.
In the 2nd of May 1808 , the figure stabbing the horse taking part of the revolt sure resembles the figure with his arms outstretched..also in the shadow to the far let is a faint representation of a woman with a child very Madonna with child like.. I love this painting, 3rd of May, and have been fortunate to see it in person
There is another painting of Goya, a twin painting of this Third of May: the Second of May. It was a symbol of freedom, and it was used during the Civil War as a reminder of the fighting for freedom. During the restore of the painting it was discover a grafitti that said "Madrid Resiste", 'Madrid Resists' as it did one century and a half years before against those who were trying to take away their freedom. So, short answer, it's more a symbol of freedom than propaganda.