Here are the different shipping companies that existed then and which is also available today.

Cunard - Website

Was founded in 1840 as the British and North American Royal Mail Steam Packet Company. The shipping company is still exists today. Cunard website

White Star Line

Was founded in 1845 in Liverpool out of John Pilkington and Henry Wilson, Oceanic Steam Navigation Company. Carrier bought 1934 Cunard out.
The Company does not currently exist but their headquarters are still there in Liverpool.

Hamburg American Line

Was founded in Hamburg, Germany in 1847 out of Albert Ballin Adolph Godeffroy, Ferdinand Laeisz, Carl Woermann with several others. The Company does not exist today.

Red Star Line

Was founded in 1871 out of Philadelphia Clement Griscom. Between 1935 and 1939, where the company's ships bought in and then walked them with their old rival
Holland America Lijn Rotterdam the Netherlands.

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