Root was an independent organization directly under Danzō. It was not subject to the Hokage's control, and though it was called an Anbu training division, it was not under the Anbu's jurisdiction either. Its uniform was a plain white or black cloak. From the Nine-Tails incident to the Uchiha massacre, this organization had been highly active and played a unique role in Konoha. However, because Hiruzen could not tolerate Shimura Danzō turning people into killing machines, after the Uchiha massacre, he stripped Danzō of his position as "Hokage's Advisor" and ordered Root disbanded. Yet after the Third Hokage died, the organization appeared once more. By the looks of it, Koharu and the others must have supported it. After all, Tsunade did not suit the tastes of those old people very well.
However, because its members took orders directly from Danzō rather than the Hokage, Li did not think this organization could truly stir up much trouble in the future. After all, no leader would support having a military force beneath them that refused to obey them.
In fact, when the Fourth Hokage died and the Third returned to power, Danzō had once directed Root members under his command to carry out an assassination attempt against the Third. But at that time, a traitor emerged among Root's members—Kakashi. On the surface, Kakashi seemed as though he no longer cared about anything, but in truth, he deeply resented Hiruzen Sarutobi as Hokage. He had always believed that Hiruzen Sarutobi bore an inescapable responsibility for his father's death. On top of that, he wanted to restore his family's prosperity, so he chose Danzō's faction, which had never gotten along with the Hokage.
But in the end, he seemed to have figured some things out and revealed the entire matter to the Third Hokage.