MySQL SUM with multiple GROUP BY on same table
I'm more of a SQL Server guy, but here is a stab to get you motivated. You could use the CASE expression to help SUM() orders by certain order types.

For example:

SELECT
    idclient AS [Client ID]
   ,COUNT(value) AS [Total Orders]
   ,SUM(value) AS [Total Order Value]
   ,SUM( CASE WHEN type1 = 'some type' THEN value ELSE 0 END) AS [Order Combo 1]
   ,SUM( CASE WHEN type1 = 'some type' AND type2 = 'another type' THEN value ELSE 0 END) [Order Combo 2]
   ,SUM( CASE WHEN type1 = 'some type' AND type2 = 'another type' AND type3 = 'another type' THEN value ELSE 0 END) [Order Combo 3]
FROM 'test'.'orders'
GROUP BY idclient


This will group the orders on [idclient] and will SUM([value]) the instances where certain order records meet the following conditions or combinations you specified. 

So, if a customer has an order where [type1] was Apples and [type2] was Oranges, you can SUM([value]) that was 1 under a new column called something like [Apple/Orange Orders].

The result can also include additional combinations for the same record in multiple fields/columns. If that is a problem, just move the CASE to the GROUP BY to break each combination into a separate record in the the result set.

Hope this helps!