Sorting part of a sheet

I need to sort groups of rows, which are contiguous and defined by a cell value. The sorting has to be confined to the group.
The attached worksheet shows this. I need to sort the values in ColI when the cells in Col H = 3. The rest of the sheet should not be affected.
In essence I need a sort function that is equivalent to the SUMIF function. I don,t mind if the solution involves VBA or if someone can construct a spreadsheet function. I have been struggling with this with no succes for hours, so help would be appreciated.
John