A question on the partitions of 1000 into six parts, and how these relate to each other

Question

There are nearly 12 billion (11,835,956,777 to be exact) partitions of 1000 into six parts.

1. If each of the six parts of any of these partitions is taken as the vertex of a loopless graph, two of which are joined by an edge if they are not relatively prime, how many of those partitions correspond to the following graph:

2. Of all 156 graphs on six vertices, is the above the one with the least positive number of partitions into six parts so attached to it?