Ortho splines between nodes in subgraphs

I am trying to connect the nodes C at the bottom of in the left cluster/subgraph to the node D at the top of the right cluster as shown in the code below:

digraph G {
    compound  = true
	
	subgraph left_cluster
	{
		subgraph first_cluster{
			A[]
		}

		subgraph second_cluster{
			B[]
		}
		
		subgraph third_cluster{
			C[]
		}
		
		A -> B[style = invis]
		B -> C[style = invis]
	}

	subgraph left_cluster
	{
		subgraph first_cluster{
			D[]
		}

		subgraph second_cluster{
			E[]
		}
		
		subgraph third_cluster{
			F[]
		}
		
		D -> E[style = invis]
		E -> F[style = invis]
	}
	
	//C -> D[splines=ortho]
}

Prior to the connection the output looks like this

Unfortunately the connection stacks both subgraphs as shown below instead of leaving them side-by-side

example-1

The following edit shows what I would like to achieve

Please advise.

It is not clear that this graphs needs clusters, but they work. That said:

  • cluster names must start with the string cluster (see below)
  • the nested subgraphs/pseudo-clusters don’t accomplish anything. I removed
  • the splines attribute has to apply to the entire graph, not individual edges
  • clusters are normally enclosed in a rectangle, peripheries=0 removes the rectangle
digraph G {
    //compound  = true  // not needed for this graph
    splines=ortho       // must apply to entire graph
    nodesep=.55  	// increase distance between the columns
	subgraph clusterL
	{
		peripheries=0  // do not draw rectangle around the cluster
		A -> B[style = invis]
		B -> C[style = invis]
	}

	subgraph clusterR
	{
		peripheries=0  // do not draw rectangle around the cluster
		D -> E[style = invis]
		E -> F[style = invis]
	}
	
	C -> D  [constraint=false]  // do not use this edge for ranking
}

Giving: