Set nodes from left to right, and other - from top to bottom on the same rank

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This is a common request and to-date there is no guaranteed “fix”.
After many failed attempts, here is a pretty clean solution. It uses constraint=false, rank=same, and the group attributes.
[the input has also been edited to make it easier for me to read]

digraph {
rankdir=LR;
node[style=filled, fillcolor=white]

// success by using both group & constraint

subgraph cluster1 {
  bgcolor=grey;

  4 [fillcolor=yellow]
  5 [fillcolor=red]
  6 [fillcolor=lightblue]
  7 [fillcolor=orange]
  8 [fillcolor=lime]
  9 [fillcolor=pink]
  11 [fillcolor=violet group=S]

  14 [fillcolor=magenta group=S]
  13 [fillcolor=lightgreen]
  12 [fillcolor=lightgrey]

  {rank=same 
  edge [constraint=false]
  4 -> 5 -> 6 -> 7  -> 8 -> 9
  }
  {rank=same 
  10 11
  }
  {rank=same  
  edge [constraint=false]
  12 -> 13 -> 14
  }

  6 -> 10
  6 -> 11
  10 -> 12
  10 -> 13
  10 -> 14
  }

1 -> 2
1 -> 3
2 -> 4
2 -> 5
2 -> 6
2 -> 7
2 -> 8
2 -> 9
14 -> 15
}

Giving:
TBLR1

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