No, it would not fit, as Typhoon is 15.96m (52ft 4in) long, 10.95m (35ft 11in) wide and 5.28m (17ft 4in) high.
The cargo bay of the C-17, which is 88 ft (26.82 m) long, 18 ft (5.48 m) wide, and 12.33 ft (3.76 m) high.
Typhoon could probably do a high speed 180 degree turn in the area occupied by a C-17.