Create Custom Attribute Group Within Custom Attribute Set Programatically On The Fly

I currently have a working method which allows me to create an attribute set on the fly. This works well:

public function createAttributeSets($attribute_set_name) {

    $attr_set_id = $this->getAttrSetId("generated_" . $attribute_set_name);

    if (!$attr_set_id) {
        $entityTypeCode = 'catalog_product';
        $entityType = $this->eavTypeFactory->create()->loadByCode($entityTypeCode);
        $defaultSetId = $entityType->getDefaultAttributeSetId();

        $attributeSet = $this->attributeSetFactory->create();
        $data = [
            'attribute_set_name' => $attribute_set_name,
            'entity_type_id' => $entityType->getId(),
            'sort_order' => 200,
        ];
        $attributeSet->setData($data);

        try {
            $this->attributeSetManagement->create($entityTypeCode, $attributeSet, $defaultSetId);
        } catch (Exception $e) {

        }

        return $attributeSet->getId();

    } else {
        return $attr_set_id;
    }

}

Now I'd like to create an attribute group within this attribute set so that it's ready to place my new attributes within it.

Is this group automatically created if I assign a new attribute to a non-existing group name when I create it?