You forgot the case where only two girls are together.
Which two girls will be together can be selected in $\binom{3}{2}$ ways. The 5 units (4 boys and 2 girls together) can be permuted in $5!$ ways and the two girls will also permute in $2!$ ways, and for the one separate girl,you will be left with 4 places to select. Hence total number of ways when only two girls are together is:
$\binom{3}{2}*5!*2*4 = 2880$
$5040 - 2880 - 720 = 1440 $