Co nuclear quadrupole resonance (NQR) measurements were performed on several superconducting (SC) Na(x)CoO(2)(.)yH(2)O samples with different values of a SC transition temperature (T,). The measurements were done for the investigation of the relationship between T, and microscopic physical quantities derived from the Co NQR. We measured Co-NQR frequency v(Q) and the nuclear-lattice relaxation rate 1/T-1 at the Co site, and found the relationship between v(Q) and the value of 1/T1T at T-c: the higher-T-c sample possesses the higher v(Q) and larger value of 1/T1T at T-c. When v(Q) exceeds a critical value (similar to 12.45 MHz), magnetic ordering was observed. A possible phase diagram in Na(x)CoO(2)(.)yH(2)O is proposed, in which the NQR frequency v(Q) is the tuning parameter and determines the ground states. In this phase diagram, the SC phase is adjacent to the magnetic phase, suggesting that the superconductivity is intimately related to magnetic fluctuations. We found the coexistence of the superconductivity and the magnetic ordering in the same sample with the highest v(Q).