The Basilisk itself was never a Horcrux, though Harry destroyed one Horcrux (the diary) by using a Basilisk fang. The seven actual Horcruxes were: Tom Riddle's diary, Marvolo Gaunt's ring, Salazar Slytherin's locket, Helga Hufflepuff's cup, Rowena Ravenclaw's diadem, Harry Potter (unintentional), and Nagini the snake. The diadem (listed as 'Daidem') was indeed a Horcrux.