When using VLOOKUP, you can only search one column and return a value from a column to the RIGHT of that column. Based on your formula, you're looking up the date in D10 in a table spanning A1:I6, so VLOOKUP is going to search column A for that date, and return the value from the second column.
Of course, this doesn't work because column A in your table doesn't contain dates. To lookup a value in one column and return a value from a column to the LEFT of it, use INDEX/MATCH, like so:
This searches I2:I6 for the value in D10, and if found will return the value from column B in the same row as the match. Change your ranges accordingly.
Assume your raw data occupies A1:C5, Enter grp1 in D1, enter date in E1
Place formula in A7
=index($b$2:$b$4,small(if($a2:$a$4=$d$1,if($c$2:$c$4=$e$1,row($b$2:$b$4)-row($b$2)+1)),rows($a$7:a7))). Use CSE copy down.
This will list all items meeting criteria of grp1 and specific date