small corporations

(xxxさんかのyyy) (Literally, ” a yyy under the umbrella of xxx”.)  A company which has been taken over by a bigger company.  Often this means companies that started out independent and got eaten in an unfriendly takeover.
(こがいしゃ) Literally, a “child corporation.” Unlike 傘下, a 子会社 is usually a company which was formed by the first corporation to carry out some specialized duty related to that corporation (i.e. a record label starts a fashion line, a legitimate bank starts an exploitive check-cashing operation in the ghetto, a house-cleaning service starts a temp corporation to hire maids). Their employees are loyal in a way that 傘下 employees are not.