Divide WP_Query posts by date & post type

Question

I have a WP_Query that divides 2 Posts types by date but the functionality is not there. Currently it outputs the dates and posts on the same level like..

-Date
-Post
-Post
-Date
-Post
-Post

What I would like is to wrap each date and its associated posts inside a div, as well as split the two post types for each date into two columns.

Update

I managed to split the posts up by date and wrap them in separate divs, now I just need to figure out how to divide the two CPTs into separate columns under each date

Updated Query

<?php
$day_check = '';
$index = new WP_Query( array(
   'orderby'=>'post_date',
   'post_type' => array('cpt1', 'cpt2'),
   'posts_per_page' =>12));
while ( $index->have_posts() ) : $index->the_post();
   $day = get_the_date('j');
   if ($day != $day_check) {
      if ($day_check != '') {
         echo '</div></div>'; // close the divs
      }
      echo '<div class="day"><div class="date">' . get_the_date() . '</div><div class="posts">';
   }?>
   <li class="post"><?php the_title(); ?></li>
<?php $day_check = $day; endwhile; ?>
<?php if ( $index->have_posts() ) :?>                                         
<?php endif; ?>

Answer 1

The post_type isn't really a meta query - therefore, both of these post_types would at least 1 category added/queried in order to get the filter invoked - using plain SQL is still a last resort.

add_filter( 'posts_groupby', 'my_posts_groupby' );

function my_posts_groupby($groupby) {
   global $wpdb;
   $groupby = "{$wpdb->posts}.post_date";
   return $groupby;
}

According to your example (I'd guess one can pass it like that as well):

$args = array(
   'posts_per_page' => 10, 
   'orderby' => 'date',
   'groupby' => 'date', /* unsure about the parameter, should be easy to find out */
   'post_type' => array('type1', 'type2')
);