You can set up a relationship to get to your three sub totals by computing totals of related records via either a filtered portal (Requires FileMaker 11) or 3 distinct relationships that include a field that matches by type as well as by QuoteID to get your three totals.
Here's the filtered portal approach.
Assuming your layout is based on LineItems with this relationship:
Quotes::QuoteID = LineItems::QuoteID
Use the duplicate button (two green plus signs) in Manage | Database | relationships to make a new occurrence of LineItems and link it like this:
LineItems::QuoteID = LineItemsSameQuote::QuoteID
Define a summary field in line items for your total. (You should already have this field for the upper part of your report.)
Put a portal to LineItemsSameQuote on your layout and select this summary field from the same table occurrence. Give it this portal filter:
LineItemsSameQuote::Type = "hardware"
and you'll get the total of all line items of type "hardware" for this quote. You can then repeat this process to add two more portals to LineItemsSameQuote, but with different portal filter expressions to get the other two totals.