Clusters of half turn metric distance 20 positions separated by a single move or premove.
These were found by searching for neighbors of the positions in this list (current size 1,029,362). Any bias in how those positions were sampled will also be reflected here.
The self-symmetry count is out of 96 total, including antisymmetry.
   # |  Nodes | Edges | Self-sym | Examples 
-----+--------+-------+----------+----------
   1 |      2 |     1 |        8 |      214
   2 |      2 |     1 |        8 |      111
   3 |      2 |     2 |       16 |      185
   4 |      2 |     2 |       16 |      104
   5 |      2 |     2 |        4 |       35
   6 |      2 |     2 |       16 |       30
   7 |      2 |     2 |       16 |       10
   8 |      2 |     2 |       16 |        6
   9 |      2 |     2 |       16 |        3
  10 |      2 |     2 |        4 |        2
  11 |      3 |     2 |       16 |       36
  12 |      3 |     2 |        4 |       31
  13 |      3 |     2 |       16 |       30
  14 |      3 |     2 |        8 |       16
  15 |      3 |     2 |        8 |        9
  16 |      3 |     2 |       16 |        6
  17 |      3 |     2 |        8 |        5
  18 |      3 |     2 |        8 |        5
  19 |      3 |     2 |        2 |        3
  20 |      3 |     2 |        8 |        1
  21 |      3 |     3 |        8 |        3
  22 |      3 |     3 |        4 |        1
  23 |      3 |     3 |        2 |        1
  24 |      3 |     4 |       32 |        9
  25 |      3 |     4 |       32 |        5
  26 |      3 |     4 |       16 |        2
  27 |      3 |     4 |        8 |        2
  28 |      3 |     4 |       16 |        1
  29 |      3 |     4 |       16 |        1
  30 |      3 |     4 |        8 |        1
  31 |      3 |     4 |        4 |        1
  32 |      3 |     6 |       16 |        5
  33 |      3 |     6 |       16 |        2
  34 |      3 |     6 |       16 |        1
  35 |      3 |     6 |       16 |        1
  36 |      4 |     4 |       16 |       23
  37 |      4 |     4 |       16 |       16
  38 |      4 |     4 |       16 |        5
  39 |      4 |     4 |       32 |        3
  40 |      4 |     4 |       16 |        1
  41 |      4 |     4 |        8 |        1
  42 |      4 |     4 |       16 |        1
  43 |      4 |     4 |       32 |        1
  44 |      4 |     4 |       32 |        1
  45 |      4 |     4 |       16 |        1
  46 |      4 |     4 |       16 |        1
  47 |      4 |     4 |        2 |        1
  48 |      4 |     6 |       16 |        1
  49 |      4 |     8 |       32 |        4
  50 |      4 |     8 |       32 |        3
  51 |      4 |     8 |        8 |        3
  52 |      4 |     8 |       16 |        1
  53 |      4 |     8 |       16 |        1
  54 |      4 |     8 |        8 |        1
  55 |      4 |     8 |       16 |        1
  56 |      4 |    12 |       16 |        2
  57 |      5 |     4 |        8 |        1
  58 |      5 |     4 |        4 |        1
  59 |      5 |     4 |       16 |        1
  60 |      5 |     6 |        8 |        1
  61 |      5 |     6 |        8 |        1
  62 |      5 |     6 |       16 |        1
  63 |      5 |     6 |       16 |        1
  64 |      5 |     8 |       16 |        1
  65 |      6 |     6 |        4 |        1
  66 |      6 |     8 |       16 |        5
  67 |      6 |     8 |       16 |        4
  68 |      6 |     8 |        8 |        2
  69 |      6 |     8 |       32 |        2
  70 |      6 |     8 |       32 |        2
  71 |      6 |     8 |        8 |        1
  72 |      6 |     8 |       16 |        1
  73 |      6 |    10 |       16 |        1
  74 |      6 |    12 |       16 |        2
  75 |      6 |    12 |       16 |        1
  76 |      6 |    12 |       16 |        1
  77 |      7 |     8 |        8 |        1
  78 |      8 |     8 |       16 |        3
  79 |      8 |     8 |       16 |        1
  80 |      8 |     8 |       32 |        1
  81 |      8 |    10 |        8 |        1
  82 |      8 |    12 |        8 |        1
  83 |      8 |    12 |        8 |        1
  84 |      8 |    12 |       16 |        1
  85 |      8 |    16 |       32 |        2
  86 |      8 |    16 |       16 |        1
  87 |      8 |    16 |       16 |        1
  88 |      8 |    24 |       32 |        1
  89 |      9 |    24 |       16 |        1
  90 |     10 |    12 |        8 |        1
  91 |     10 |    14 |        8 |        1
  92 |     10 |    22 |        8 |        1
  93 |     10 |    24 |       16 |        1
  94 |     11 |    14 |        4 |        1
  95 |     11 |    30 |       16 |        1
  96 |     12 |    16 |       32 |        2
  97 |     12 |    16 |       32 |        2
  98 |     12 |    16 |        8 |        1
  99 |     12 |    20 |        8 |        1
 100 |     12 |    24 |        8 |        1
 101 |     18 |    28 |       16 |        1