The arrangement of nucleosomes inside chromatin is of extensive interest. While in vitro experiments have revealed the formation of 30 nm fibers, most in vivo studies have failed to confirm their presence in cell nuclei. To reconcile the diverging experimental findings, we characterized chromatin organization using a near atomistic model. The computed force-extension curve matches well with measurements from single-molecule experiments. Notably, we found that a dodeca-nucleosome in the two-helix zigzag conformation breaks into structures with nucleosome clutches and a mix of trimers and tetramers under tension. Such unfolded configurations can also be stabilized through trans interactions with other chromatin chains. Our study supports a hypothesis that disordered, in vivo chromatin configurations arise as folding intermediates from regular fibril structures. We further revealed that chromatin segments with fibril or clutch structures engaged in distinct binding modes and discussed the implications of these inter-chain interactions for a potential sol-gel phase transition.