Termites can also reproduce asexually.

From Science Daily:

Scientists at North Carolina State University and three universities in Japan have shown for the first time that it is possible for certain female termite "primary queens" to reproduce both sexually and asexually during their lifetimes.

The asexually produced babies mostly grow to be queen successors – so-called "secondary queens" – that remain in the termite colony and mate with the king. This produces large broods of babies without the dangers of inbreeding, as secondary queens have no genes in common with the king.

Babies produced the old-fashioned way, between either the primary or secondary queens and the king, are mostly workers and soldiers of both genders, the research shows.