Recent experimental studies proved the presence of the triplet spin state in atomically precise heptauthrene nanostructure of nanographene type (composed of two interconnected triangles with zigzag edge). In the paper, we report the computational study predicting the possibility of controlling this spin state with an external in-plane electric field by causing the spin switching. We construct and discuss the ground state magnetic phase diagram involving S=1 (triplet) state, S=0 antiferromagnetic state and non-magnetic state and predict the switching possibility with the critical electric field of the order of 0.1 V/Å. We discuss the spin distribution across the nanostructure, finding its concentration along the longest zigzag edge. To model our system of interest, we use the mean-field Hubbard Hamiltonian, taking into account the in-plane external electric field as well as the in-plane magnetic field (in a form of the exchange field from the substrate). We also assess the effect of uniaxial strain on the magnetic phase diagram.