Alphabetical list custom tags -> even if empty

Hello there

I created some code which returns an alphabetical list/index of custom tags and filters the custom posts in a grid layout. The tags are named as “tagdirectory”. The custom post is named “directory”.

This is the code:

<?php
$list = '';
$tags = get_terms( 'tagdirectory' );
echo '<ul id="portfolio-filter">';
echo '<li><a href="#all" title="">All</a></li>';
$groups = array();
if( $tags && is_array( $tags ) ) {
foreach( $tags as $tag ) {
$first_letter = strtoupper( $tag->name[0] );
$groups[ $first_letter ][] = $tag;
}
if( !empty( $groups ) ) {
foreach( $groups as $letter => $tags ) {
$list .= "\n\t" . '<h2>' . apply_filters( 'the_title', $letter ) .'</h2>';
$list .= "\n\t" . '<ul>';
foreach( $tags as $tag ) {
$lower = strtolower($tag->name);
$name = str_replace(' ', ' ', $tag->name);
$naam = str_replace(' ', '-', $lower);
$list .= "\n\t\t" . '<li><a href="#'.$naam.'">'.$name.'</a></li>';
}
}
}
}else $list .= "\n\t" . '<p>Sorry, but no tags were found</p>';print $list;
echo "</ul>";
?>

This works perfectly but I would also like for empty letters from the alphabet to be shown.

For example, now it returns:

A
Aicher Otl
Apeloig Philippe
B
Bass Saul
F
Fitszimmons Maureen

… and so on

But it doesn’t show the empty letter groups because there are no tags starting with this letter. I do need it to show the capital letter for empty groups though, like so:

A
Aicher Otl
Apeloig Philippe
B
Bass Saul
C
D
E
F
Fitszimmons Maureen
G
… and so on

Can anybody help me and tell me what code I should add for this to work?

Thanks!