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The semantically disentangled latent subspace in GAN provides rich interpretable controls in image generation. This paper includes two contributions on semantic latent subspace analysis in the scenario of face generation using StyleGAN2. First, we propose a novel approach to disentangle latent subspace semantics by exploiting existing face analysis models, e.g., face parsers and face landmark detectors. These models provide the flexibility to construct various criterions with very concrete and interpretable semantic meanings (e.g., change face shape or change skin color) to restrict latent subspace disentanglement. Rich latent space controls unknown previously can be discovered using the constructed criterions. Second, we propose a new perspective to explain the behavior of a CNN classifier by generating counterfactuals in the interpretable latent subspaces we discovered. This explanation helps reveal whether the classifier learns semantics as intended. Experiments on various disentanglement criterions demonstrate the effectiveness of our approach. We believe this approach contributes to both areas of image manipulation and counterfactual explainability of CNNs. The code is available at \url{https://github.com/prclibo/ice}.