You can achieve this in Power BI without creating multiple measures by leveraging the built-in Matrix visual and DAX’s “Show Values as” options.
Here’s how you can do it:
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Load your data into Power BI as a simple table (as in your example).
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Create a Matrix visual:
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Drag the Group field into the Rows area.
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Drag the Type field below Group in the Rows area (to create a hierarchy).
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Drag the Count field into the Values area and set the aggregation to Sum (default).
 
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Enable subtotals to get the “Total” row for each group:
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Click on the Matrix visual, go to the Format pane, and expand the “Subtotals” section.
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Turn on “Row subtotals.” This will automatically show totals for each group, just as you expect.
 
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No need to create extra measures—Power BI Matrix will sum up the counts by Group and Type, and add totals for you.