A family of organic conductors, alpha-(BEDT-TTF)(2)MHg(SCN)(4), is known to show the density wave (DW) state for M = Tl, K, and Rb salts, or the superconducting (SC) state for M = NH4 salt at low temperatures. In contrast, alpha-(BEDT-TTF)(2)MHg(SeCN)(4) shows no phase transition and retains its metallic characteristics down to low temperatures. Since no alpha-(BEDTTTF)(2)MHg(SeCN)(4) salt shows the DW or SC states, it was unclear whether the system of alpha-(BEDT-TTF)(2)MHg(SeCN)(4) could be understood by the same phase diagram as that of alpha-(BEDT-TTF)(2)MHg(SCN)(4). Here, we succeeded in synthesizing a key material, alpha-(BEDT-TTF)(2)NH4Hg(SeCN)(4), and determined its crystal structure. The temperature dependence of its electric conductivity and spin susceptibility showed its DW state at low temperatures, indicating that the alpha-(BEDT-TTF)(2)MHg(SeCN)(4) system is linked to the alpha-(BEDTTTF)(2)MHg(SCN)(4) system. From the established phase diagram, we found that the dihedral angle between crystallographically independent A and B molecules, Theta(B), and that between A and C molecules, Theta(C), are good tuning parameters as in theta-type BEDT-TTF salts. In the Theta(B)-Theta(C) plot, the SC salt is located in the large Theta(B) and small Theta(C) regions, whereas the metallic salts are located in the small Theta(B) and large Theta(C) regions. The DW salts are located in the intermediate Theta(B) and Theta(C) regions. The relationship between their location in the Theta(B)-Theta(C) plot and the ground states supports the prediction that the local density of state between A and B molecules determines the ground states.