Republic TV is not completely owned by Asianet News.
Can be said that it's a joint venture of Arnab Goswami and Rajeev Chandrasekhar MP from Karnataka the two biggest investors in the channel.
Asianet News is owned and maintained by Jupiter Entertainment Ventures Private Limited which comes under Rajeev Chandrasekhar. Jupiter media owns Asianet News in Malayalam, Suvarna 24x7 in Kannada, Best FM, Radio Indigo and Kannada newspaper 'Kannada Prabha'
Rajeev is the biggest investor in Arnab's Republic Channel.
These are the main investors in this channel - "ARG Outlier Media - Asianet News Service"
where ARG Outlier Media is Arnab's own company. He is the CEO of ARG Outlier Media.
So as Rajeev MP is the biggest investor in Republic it's shown as Asianet Newsable.