Sorry I’m a bit late with this, but I haven’t seen this since my previous comment.
The Hand probably represents the hand of Jesus. The “finger puppets” most likely represent either saints or churches which stand on the “foundation” represented by His hand. The sheep probably represent the laity who are drinking the Blood of Christ which is, of course, the Communion. It’s basically an allegorical work designed to tell the viewer what The Church is all about and I would imagine that a contemporary church member would instantly have been able to decipher the symbolism.
LOLTheist: Blasphemy is Teh Funneh 
I *think* it’s supposed to be a parody of “The Thunderbirds are GO!”
Oh yeah, my captioning definitely was.
The painting itself… still have no idea.
Sorry I’m a bit late with this, but I haven’t seen this since my previous comment.
The Hand probably represents the hand of Jesus. The “finger puppets” most likely represent either saints or churches which stand on the “foundation” represented by His hand. The sheep probably represent the laity who are drinking the Blood of Christ which is, of course, the Communion. It’s basically an allegorical work designed to tell the viewer what The Church is all about and I would imagine that a contemporary church member would instantly have been able to decipher the symbolism.