In this paper, an extended form of generalized (2 + 1)-dimensional Hirota bilinear equation is considered which demonstrates nonlinear wave phenomena in shallow water, oceanography and nonlinear optics. We have successfully studied the integrability characteristic of the nonlinear equation in many aspects. The Painlevè integrability test is examined on the equation and found to be not integrable in Painlevè sense. The concept of Bell polynomial form is introduced and the Hirota bilinear form, Bäcklund transformations, Lax pair and infinite conservation laws are obtained systemically. We have exploited the expressions of one soliton, two soliton and three soliton solutions and demonstrated them pictorially. Further, Lie symmetry approach is applied to analyze the Lie symmetries and vector fields of the considered problem. The symmetry reductions were then obtained using similarity variables, and some closed-form solutions are secured.