slow mysql queries – group by

I have a WordPress site with over 200,000 posts. It has been running slow and we’ve narrowed the cause down to a particular SQL query (see below). Specifically the group by and order by are causing the slowness. Has anyone had the same problem? Have you been able to solve it?

SELECT SQL_CALC_FOUND_ROWS wp_posts.* FROM wp_posts INNER JOIN wp_term_relationships ON (wp_posts.ID = wp_term_relationships.object_id) INNER JOIN wp_term_taxonomy ON (wp_term_relationships.term_taxonomy_id = wp_term_taxonomy.term_taxonomy_id) WHERE 1=1 AND wp_term_taxonomy.taxonomy = ‘category’ AND wp_term_taxonomy.term_id IN (’56’, ’18’, ’32’, ’34’, ’33’, ’12’, ’40’, ’47’, ’49’, ’52’, ‘9’, ’29’, ’20’, ’17’, ‘8’, ’11’, ’28’, ’16’, ’42’, ’25’, ’55’, ’43’, ’13’, ’35’, ’26’, ’36’, ’37’, ’44’, ’51’, ’46’, ‘7’, ‘6’, ’39’, ’27’, ’10’, ’31’, ’54’, ’22’, ’23’, ’24’, ’48’, ’15’, ’14’, ’53’, ’41’, ’21’, ’30’, ’19’, ’45’, ’50’, ’38’) AND wp_posts.post_type = ‘post’ AND (wp_posts.post_status = ‘publish’ OR wp_posts.post_status = ‘private’) GROUP BY wp_posts.ID ORDER BY wp_posts.post_date DESC LIMIT 0, 20