In this paper, we address the problem of 6-DoF object pose estimation from a single RGB image. Indirect methods that typically predict intermediate 2D keypoints, followed by a Perspective-n-Point solver, have shown great performance. Direct approaches, which regress the pose in an end-to-end manner, are usually computationally more efficient but less accurate. However, direct pose regression heads rely on globally pooled features, ignoring spatial second-order statistics despite their informativeness in pose prediction. They also predict, in most cases, discontinuous pose representations that lack robustness. Herein, we therefore propose a covariance-pooled representation that encodes convolutional feature distributions as a symmetric positive definite (SPD) matrix. Moreover, we propose a novel pose encoding in the form of an SPD matrix via its Cholesky decomposition. Pose is then regressed in an end-to-end manner with a manifold-aware network head, taking into account the Riemannian geometry of SPD matrices. Experiments and ablations consistently demonstrate the relevance of second-order pooling and continuous representations for direct pose regression, including under partial occlusion.