view subcategories order by id

by

If you want to order by id you can replace

 $subcategories = get_terms( 'category' , 'parent=".get_query_var("cat') );

with

 $args=array(
     'parent'=>get_query_var('cat'),
     'orderby' => 'id', 
     'order' => 'ASC',  
 );
 $subcategories = get_terms( 'category' , $args);

You can read more about the available parameters in the Codex here:

http://codex.wordpress.org/Function_Reference/get_term