IPA: /ˌɪn.səˈbɔː.dɪ.nət.li/
KK: /ˌɪn.səˈbɔːr.dɪ.nət.li/
In a way that shows a lack of respect for authority or rules; disobediently.
The employee acted insubordinately by refusing to follow the manager's instructions.
Insubordinately → It is formed from "in-" (meaning not), "subordinare" (from Latin, meaning to arrange under), and "-ly" (meaning in a manner). The word describes behaving in a manner that is not submissive or obedient to authority.
Think of 'not' ('in-') being 'under' ('subordinare') authority — that's why insubordinately means acting in a way that defies authority.