The Sword of Rao, also known as the "Zod Loyalists", is the main antagonistic faction of Man of Steel. It is a revolutionary political movement that sought to overthrow the Kryptonian Law Council and bring Krypton back to its former glory. After the planet's destruction, all of its members were released from their imprisonment in the Phantom Zone and eventually headed towards Earth where they sought to destroy it and bring rebuild Kryptonian civilization and have Earth be the new Krypton. This organization was named after a Kryptonian sun god Rao.
The Sword of Rao was founded at some point in time back during Krypton's existence. They were made up of extremist members of the Kryptonian Warrior Guild who viewed the high council as being weak and corrupt as well as weakening Krypton's bloodline. They eventually gained more members and Zod became the leader.
During the final moments of Krypton, General Zod and members of the Sword of Rao, assaulted the capital city of Kandor where they are first seen overthrowing the entire council. Zod approaches Jor-El who was speaking to the council and tried to convince him to join his side. He eventually rejected and escaped where Zod and his forces chased after him. Zod's troops eventually followed Jor-El to his home where they confront him after it is revealed that the Growth Codex was sent away along with their son, Kal-El. Furious, Zod takes out a knife and impales Jor-El and effectively kills him moments before the Kryptonian Military arrives and arrests Zod and his men. They're brought before the council where they are sent to three hundred years in the Phantom Zone and are eventually set off to the Black Zero but not until Krypton had been destroyed.
Restoration and Revival
Following the destruction fo Krypton, the Balck Zero ship sending Zod and his men to the Phantom Zone and deactivated sometime during the journey where all of Zod's men and himself were free. They eventually saw the destroyed remains of Krypton and eventually restarted the ship and repurposed it as the new headquarters for the Sword of Rao. Zod also gathered traces of Krypton's remains and would use them to terraform a planet and make it a new Krypton.
Invasion of Earth
After Zod reactivated the Black Zero ship, they eventually tracked Superman back to Earth where they threatened the planet had they not handed him over. Superman turned himself in and was eventually met with Zod where he tried to convince him to join Zod in rebuilding Krypton but unfortunately, however, it would cost the life of Earth and his home so Superman rejected it. This eventually leads to the Sword of Rao invading Earth where their ships ravaged both sides of the planet in an attempt to terraform the earth into making it a new Krypton. After one of the leading scientists of the organization found out that Superman had the codex all along, Zod realized that he could kill Superman and extract his DNA so that he could terraform the destroyed Earth and ordered the Sword of Rao to invade.
The invasion began when Zod's forces began leveling the planet on both sides of the world with two ships on both of Earth's hemispheres. This eventually leads to the United States Military to take on the one ship in Metropolis and Superman dealt with the one on the Indian Ocean. Superman dealt with his and eventually faced off against Zod where much of Metropolis was destroyed and Zod was eventually killed. In the aftermath, the remaining members of the Sword of Rao where all imprisoned and sent back to the Phantom Zone once more leaving the organization technically inactive, but currently disbanded.