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($domain) = split '/', $string;
$wanted = (split /\./, $domain)[-2];
...
# or

$wanted = (split /\./, (split '/', $string)[0])[-2];

($wanted) = $string =~ m{
  ( [^.]+ )   # save the non-. sequence to $1
...
  [^./]+      # the final non-. non-/ sequence
  (?: / | $)  # / or the end of the string
}x;