Synergies

21st Century Fox owns

Fox Networks (A unit of Fox Networking Group)

FX Networks and Productions (FX, FXX, FXM)

National Geographic Channel

Nat Geo WILD

Nat Geo Mundo

Fox Sports Network (FSN) and 22 regional cable sports networks

FOX Sports 1

FOX Sports 2

FOX Soccer Plus

FOX College Sports

FOX Deportes

FOX Life

Baby TV

BTN (co-venture with the Big Ten Conference)

(Digital Extensions of Fox Networks:)

BTN2Go

FOX Sports GO

FXNOW

Nat Geo TV

Big Ten Network (A joint venture between the Big Ten Conference and Fox Networks)

Fox Business Network

Fox Deportes

Fox News Channel

Twentieth Century Fox Film

Twentieth Century Fox

Fox 2000 Pictures

Fox Searchlight Pictures

Fox International Productions

Twentieth Century Fox Animation

Twentieth Century Fox Television

The Fox News and Fox Business Network work together. The Fox Network and FX Networks work together, often sharing the same shows. The National Geographic Channel works independently as a Partner company. The Sports channels have the most extensive synergies. They also own and operate the social media account.
The synergies result in a more profitable media production. For example, fox can produce one show and put it on the FOX cable channel and then later put it on FX or FXX. They include clips of shows in their social media accounts to promote the programming that is on that night.
Synergies can definitely have negative effects. For example, FOX News supports views that aren't as environmentally conscious as National Geographic. This might influence the content that Nat. Geo. produces.