Coupled states of cold <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">Yb</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>174</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow>

We experimentally and theoretically study the formation of dressed states emerging from strong collective coupling of the narrow intercombination line of Yb atoms to a single mode of a high-finesse optical cavity. By permanently trapping and cooling the Yb atoms during their interaction with the cavity, we gain continuous experimental access to the dressed states. This allows us to detect both their field and their atomic properties, by simultaneously measuring the steady-state cavity transmission and free-space fluorescence. By varying the cavity and probe frequencies, we observe coupled atom-cavity states with atom-number-dependent splitting, the hallmark of collective strong coupling of the atoms with the single cavity mode. We find additional fluorescence output at atomic resonance, which we explain by the effects of dephasing and inhomogeneous broadening. We compare our experimental results with a theoretical model and find good qualitative agreement.