Brain hemorrhage (BH) is a severe type of stroke resulting in high mortality and morbidity. Detection and diagnosis of BH is commonly performed using neuroimaging tools such as Computed Tomography (CT). We compare and contrast symmetry-aware, symmetry-naive feature representations and their combination for the detection of BH using CT imaging. One of the proposed architectures, e-DeepSymNet, achieves AUC 0.99 [0.97- 1.00] for BH detection. An analysis of the activation values shows that both symmetry-aware and symmetry-naive representations offer complementary information with symmetry-aware representation naive contributing 20% towards the final predictions.