Order authors list alphabetically, according to Display_Name

it sucks but it seems this is impossible to do. anyone has any suggestions?

function contributors() {
    global $wpdb;

    $authors = $wpdb->get_results("SELECT ID, user_nicename from $wpdb->users WHERE display_name <> 'admin' ORDER BY display_name");

    foreach ($authors as $author ) {

    echo "<li>";
    echo "<a href=\"".get_bloginfo('url')."/author/";
    the_author_meta('user_nicename', $author->ID);
    echo "/\">";
    echo get_avatar($author->ID);
    echo "</a>";
    echo '<div>';
    echo "<a href=\"".get_bloginfo('url')."/author/";
    the_author_meta('user_nicename', $author->ID);
    echo "/\">";
    the_author_meta('display_name', $author->ID);
    echo "</a>";
    echo "<br />";
    echo "Website: <a href=\"";
    the_author_meta('user_url', $author->ID);
    echo "/\" target='_blank'>";
    the_author_meta('user_url', $author->ID);
    echo "</a>";
    echo "<br />";
    echo "Twitter: <a href=\"https://twitter.com/";
    the_author_meta('twitter', $author->ID);
    echo "\" target='_blank'>";
    the_author_meta('twitter', $author->ID);
    echo "</a>";
    echo "<br />";
    echo "<a href=\"".get_bloginfo('url')."/author/";
    the_author_meta('user_nicename', $author->ID);
    echo "/\">Visit&nbsp;";
    the_author_meta('display_name', $author->ID);
    echo "'s Profile Page";
    echo "</a>";
    echo "</div>";
    echo "</li>";
    }
    }