Featuring exotic quantum transport and surface states, topological semimetals can be classified into nodal-point, nodal-line, and nodal-surface semimetals according to the degeneracy and dimensionality of their nodes. However, a topological semimetal that possesses both nodal points and nodal lines is rarely reported. Here, we propose a scheme to construct this type of topological semimetal, which simultaneously exhibits hinge Fermi arcs and drumhead surface states. Then, by applying periodic driving on the system, we find a hybrid-order topological semimetal with nodal points and rich nodal-line structures and its conversion into a first-order topological semimetal, which are absent in a static system. Our results enrich the family of topological semimetals, and establish a foundation for further exploration of their potential applications.

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• Dirac semimetal
• Floquet systems
• Nodal-line semimetals
• Topological materials