How to get Shipment method wise suppliers with most order quantity?

I am having difficulties to understand when to use subqueries and how to implement them in a way that makes sense.

I have the following tables:

Table supplier:

Table orderitem:

I want to find the supplier with the highest amount of shipped order_items for each shipping method. So my end result should look this:

I came up with this:

SELECT 
    SHIPPINGMETHOD, SUPPLIERNAME, COUNT(ORDER_ID) AS AMOUNT
FROM 
    ORDERITEM
JOIN 
    SUPPLIER L ON L.SUPPLIER_ID = ORDERITEM.SUPPLIER
GROUP BY 
    SHIPPINGMETHOD, SUPPLIERNAME;

But this only returns the amount of shipped items of each supplier of each shipping method.

So then I tried this:

SELECT 
    SHIPPINGMETHOD, L.SUPPLIERNAME, COUNT(OI.ORDER_ID) AS AMOUNT
FROM 
    ORDERITEM AS OI
JOIN 
    SUPPLIER L ON L.SUPPLIER_ID = OI.SUPPLIER
GROUP BY 
    OI.SHIPPINGMETHOD, L.SUPPLIERNAME
HAVING 
    COUNT(OI.ORDER_ID) = (SELECT MAX(AMOUNT)
                          FROM 
                              (SELECT 
                                   OI2.SHIPPINGMETHOD, L2.SUPPLIERNAME, 
                                   COUNT(OI2.ORDER_ID) AS AMOUNT
                               FROM 
                                   ORDERITEM AS OI2
                               JOIN 
                                   SUPPLIER L2 ON L2.SUPPLIER_ID = OI2.SUPPLIER
                               GROUP BY 
                                   OI.SHIPPINGMETHOD, L.SUPPLIERNAME) AS SUB
);

I only get one row back. The row shows the correct supplier and the correct amount of shipped items for one of the methods, but I expected 5 rows. I feel like I am very close, but honestly have no clue at all what my mistake actually is.

If you are trying to find shipping method wise suppliers with highest order quantity then you can try this:

** here row_number()over() window function is used to rank the supplier in descending order of order quantity.

Query:

with cte as 
(
SELECT shippingmethod, L.name suppliername , COUNT(order_id) AS AMOUNT,
row_number()over(partition by shippingmethod, L.name order by COUNT(order_id) desc) as rn 
FROM orderitem
JOIN supplier L on L.supplier_id = orderitem.SUPPLIER
GROUP BY shippingmethod, L.name
)
select shippingmethod, suppliername , AMOUNT from cte
where rn=1

Output:

fiddle

*** If there are more than one customer with highest order quantity all of those would be in the list.