How to arbitrarily specify a face of planar graph as an external surface and draw it?

I learned this theorem in the graph theory textbook.

Theorem Every $ 2$ -connected plane graph can be embedded in the plane so that any specified face is the exterior.

G=PlanarGraph[{1 <-> 2, 1 <-> 3, 1 <-> 4, 2 <-> 3,               3 <-> 4, 2 <-> 5, 5 <-> 6, 6 <-> 3},               VertexLabels -> All] 

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In the above embedding of this graph, we know $ 1256341$ is boundary exterior face of $ G$ .

I don’t know if there is a way to make the triangle face $ \Delta_{134}$ outside.

The above is just an example. For the graph $ G$ , maybe I can change the layout of some points by VertexCoordinates. But for the large number of vertices, I don’t know if there is a good and unified way to arbitrarily specify an external face and give a good plane drawing.