Question: How to draw the relation of the extension field

This code can draw the subgroup lattice:

DrawSubgroupLattice(GaloisGroup(x^3 - 2, x), 'indices')

But I really want to know what the extension of field about each subgroup corresponds to, like this:

The root of the polynomial r1=21/3, r2=21/3(-1+sqrt(3) I)/2, r2=21/3(-1-sqrt(3) I)/2 in the above graph. Further, how do we draw the extension relation of this polynomial:


The maple can draw this graph? If maple can't draw it, what software can?

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