India’s largest conglomerate, Tata Group, is headed for an internal showdown as it wrestles with the question of who will lead its holding company Tata Sons Pvt., which is under regulatory pressure to go public.

The Indian banking regulator’s refusal to exempt Tata Sons Pvt. from a public listing-rule comes as an unexpected blow for group patriarch Noel Tata, who’s already struggling to address leadership uncertainty at the top of the $185 billion conglomerate.