These Middle Silurian Period corals are called Cladopora (Coenites) ordinata. They were found in Louisville, Kentucky in the Louisville Limestone. This specimen is described in Erwin Stumm's Silurian and Devonian Corals of the Falls of the Ohio on page 75 and in plate 69 figures 4,7,9,11, and 12. He describes it as, "Corallum typically dendroid, branching biserially, composed of corallites diverging radially from axes of stems and directed obliquely upward toward periphery. Stems 2-4 mm in diameter. Apertures sublunate, averaging about 0.5 mm in diameter and having prominent lower lip. Mural pores apparently absent."
This piece is rather large from what I normally find. The coral fragment is usually about the size of an American half dollar or quarter coin. This Coenites appears to be growing on a stromatoporoid or is it the other way around?