Companies, Units, Regiments...math.

If I understand correctly, multiple Companies = Regiment (a.k.a., Unit). How many companies would typically be in a single regiment/unit?

Two of my ancestors served in Illinois:

1. S.W. Jackson, 88th IL Infantry, Co. E
2. George Hosier, 93rd IL Infantry, Co. I

I have CMSRs, carded medical, and pension files for both men; am simply curious about how the nested military groups fit within one another. Here's a graphic found online (source: Civil War Army Organization | Civil War Trust). Would companies be the next layer at the top of the chart?