Why are there 6 automorphisms for this graph?

Question

    o 
    |
o---o---o---o
 \         /
  o       o
   \     / \
    o   o   \
   / \ /     o
  /   o
 o

(I apologise for the poor diagram unable to insert an image yet)
o represents a node and the dashed lines are arcs
My question is why are there 6 automorphisms for this graph? I can only identify 3 due to rotational symmetry.

Answer 1

This one has few enough points that we can draw a picture with the same geometric symmetries as the graph automorphisms. A rare luxury