<?php
//# first of all, you need to get the category array,
//   and I did it, putting the line bellow inside the loop
$category = get_the_category(get_the_ID());

// once you have the category array, the rest of the code will work wherever you want on the page

//# getting the main category of the page
$catid=$category[0]->category_parent;
if($catid==0){
  $catid=$category[0]->cat_ID;
}

//# now letz get the children categories of the main category
$categories = get_categories('child_of='.intval($catid));

foreach ($categories as $category) {
    //# check if it is a real parent category with subcategories
    if ($category->parent ==$catid):
        echo
        '
        <div class="cat-item">
        <div class="image">'.get_cat_icon("echo=false&cat=".$category->cat_ID).'</div>
        <div class="text">
        <a href="'.get_category_link($category->term_id ).'">'.$category->cat_name.'</a>
        </div></div>
        '

        ;
        //# here we go, getting the subcategories
        $subcategories=  get_categories('child_of='.intval($category->cat_ID));
        foreach ($subcategories as $subcategory) {
            echo '<span class="subcategory" style="padding-left:12px">';
            echo '<a href="">'.$subcategory->cat_name.'</a></span>';
        }

    endif;
}

?>