BuddyPress.org

You can use the loop which is in groups-loop.php.

Try this and add some CSS class to your need to fit with your theme. code goes to bp-custom.php

function my_groups_avatar_on_profile() {

$user_id = bp_displayed_user_id();

if ( bp_has_groups( 'type=alphabetical&user_id=' . $user_id ) ) : ?>

<div style="clear:both;">
	<ul>	
		<?php while ( bp_groups() ) : bp_the_group(); ?>	

			<li style="">
				<div>
					<a href="<?php bp_group_permalink() ?>"><?php bp_group_avatar_thumb() ?></a>
				</div>
			</li>
	
		<?php endwhile; 
endif; ?>

	</ul>
</div>
<?php
}
add_action ( 'bp_after_member_header', 'my_groups_avatar_on_profile' );

You’re welcome.