Countless low-surface brightness objects-including spiral galaxies, dwarf galaxies, and noise patterns-have been detected in recent large surveys. Classically, astronomers visually inspect those detections to distinguish between real low-surface brightness galaxies and artefacts. Employing the Dark Energy Survey (DES) and machine learning techniques, Tanoglidis et al. (2020) have shown how this task can be automatically performed by computers. Here, we build upon their pioneering work and further separate the detected low-surface brightness galaxies into spirals, dwarf ellipticals, and dwarf irregular galaxies. For this purpose we have manually classified 5567 detections from multi-band images from DES and searched for a neural network architecture capable of this task. Employing a hyperparameter search, we find a family of convolutional neural networks achieving similar results as with the manual classification, with an accuracy of 85% for spiral galaxies, 94% for dwarf ellipticals, and 52% for dwarf irregulars. For dwarf irregulars-due to their diversity in morphology-the task is difficult for humans and machines alike. Our simple architecture shows that machine learning can reduce the workload of astronomers studying large data sets by orders of magnitudes, as will be available in the near future with missions such as Euclid.