Aqueous solutions of a nonionic surfactant, n-dodecylhexaoxyethylene glycol [C12H25 (OCH2CH2)(6) OH], termed C12E6, have been studied in the mole ratio range W-0 = 5.6-14.9, where W-0 = [D2O]/[C12E6]. There, below a given temperature, a smectic lamellar phase exists. As shown by H-1 and H-2 NMR spectra, cooling induces the isotropic phase to become an almost completely isooriented lamellar phase when the magnetic field strength is high (14.1 T). In presence of high magnetic fields, the phase diagram is slightly different with respect to the originally reported one, and the coexistence of an isotropic phase and of the isooriented lamellar one can be observed. In a wide temperature range, only the isooriented lamellar phase is present; it is stable out of the magnetic field for several months. A careful study of the H-2 Splitting as a function of temperature and concentration indicates the onset of fluctuating cylinder inside the lamellar phase and defines their onset and region of existence. Optical polarizing microscopy experiments confirm the above observation, showing the occurrence of fine grained, mosaic optical textures.