The relationship between amyloid deposition and cellular toxicity is still controversial. In addition to fibril-forming oligomers, other soluble Aβ forms (amyloid β-derived diffusible ligands (ADDLs)) were also suggested to form and to present different morphologies and mechanisms of toxicity. One ADDL type, the "globulomer," apparently forms independently of the fibril aggregation pathway. Even though many studies argue that such soluble Aβ oligomers are off fibril formation pathways, they may nonetheless share some structural similarity with protofibrils. NMR data of globulomer intermediates, "preglobulomers," suggested parallel in-register C-terminal β-sheets, with different N-terminal conformations. Based on experimental data, we computationally investigate four classes of Aβ dodecamers: fibril, fibril oligomer, prefibril/preglobulomer cluster, and globulomer models. Our simulations of the solvent protection of double-layered fibril and globulomer models reproduce experimental observations. Using a single layer Aβ fibril oligomer β-sheet model, we found that the C-terminal β-sheet in the fibril oligomer is mostly curved, preventing it from quickly forming a fibril and leading to its breaking into shorter pieces. The simulations also indicate that β-sheets packed orthogonally could be the most stable species for Aβ dodecamers. The major difference between fibril-forming oligomers and ADDL-like oligomers (globulomers) could be the exposure of Met-35 patches. Although the Met-35 patches are necessarily exposed in fibril-forming oligomers to allow their maturation into fibrils, the Met-35 patches in the globulomer are covered by other residues in the orthogonally packed Aβ peptides. Our results call attention to the possible existence of certain "critical intermediates" that can lead to both seeds and other soluble ADDL-like oligomers.