  Nodal-line semimetals are commonly believed to exist in $\mathcal{PT}$
symmetric or mirror-rotation symmetric systems. Here, we find a flux-induced
parameter-dimensional second-order nodal-line semimetal (SONLS) in a
two-dimensional system without $\mathcal{PT}$ and mirror-rotation symmetries.
It has coexisting hinge Fermi arcs and drumhead surface states. Meanwhile, we
discover a flux-induced second-order topological insulator (SOTI). We then
propose a Floquet engineering scheme to create exotic parameter-dimensional
hybrid-order nodal-line semimetals with abundant nodal-line structures and
widely tunable numbers of corner states in a SONLS and SOTI, respectively. Our
results break the perception of SONLSs and supply a convenient way to
artificially synthesize exotic topological phases by periodic driving.
