my $dbh = ... # set up database

sub display_groups { 
    my ( $parent, $level ) = @_;
    
    # get all children of this parent
    my $sth = $dbh->prepare("SELECT id, gname
                             FROM groups WHERE subgroup=?
                             ORDER BY gname");
    $sth->execute( $parent );

    # display each child and its descendants 
    while( my $row = $sth->fetchrow_hashref ) { 
        print " " x $level;  # indent
        print $row->{gname}, "\n";
        display_groups( $row->{id}, $level + 1 );
    }
}

# start with children of group 0
display_groups( 0, 0 );