In the realm of wireless communication, deep learning has exhibited promising outcomes across various tasks, including automatic modulation classification (AMC), channel estimation, and signal detection, yielding substantial enhancements in performance and efficiency. AMC plays a pivotal role in identifying the modulation scheme of a received signal without prior knowledge of the transmitter. However, existing AMC techniques attempt to classify both analog and digital modulations together, disregarding their distinct characteristics. In this work, we propose a multilevel approach for AMC, wherein the received signals are first classified into their parent class, i.e., analog or digital modulation, and subsequently further classified into their respective modulation type. For implementing multilevel approach, we propose three distinct deep learning models: analog digital modulation classifier (AD-MC), analog modulation classifier (An-MC), and digital modulation classifier (Dig-MC). Performance analysis is conducted for the individual models as well as for the multilevel model that integrates all three models. The multilevel model demonstrates accurate signal classification at Signal-to-Noise Ratios (SNRs) of 0 dB or higher, achieving a remarkable classification accuracy of over 90%. Furthermore, the proposed multilevel model surpasses state-of-the-art AMC methods in accuracy while maintaining lower complexity.