my %newhash;
foreach my $attribute (sort keys %sorted_by_attribute) {
  my $individual_values = $sorted_by_attribute{$attribute};
  
  foreach my $value (keys %$individual_values) {
    my @systems = @{$sorted_by_attribute{$attribute}{$value}};
    
    foreach $system (@systems) {
      my $key = $HoH{$system}{'Group'};
      my $str = sprintf "%s = > %s\n", $HoH{$system}{'System Name'}, $value;
      push @{ $newhash{$attribute}{$key} }, $str;
    }
  }
}  

print Dumper (\%newhash);