Axial coding is a commonly used qualitative analysis method that enhances document understanding by organizing sentence-level open codes into broader categories. In this paper, we operationalize axial coding with large language models (LLMs). Extending an ensemble-based open coding approach with an LLM moderator, we add an axial coding step that groups open codes into higher-order categories, transforming raw debate transcripts into concise, hierarchical representations. We compare two strategies: (i) clustering embeddings of code-utterance pairs using density-based and partitioning algorithms followed by LLM labeling, and (ii) direct LLM-based grouping of codes and utterances into categories. We apply our method to Dutch parliamentary debates, converting lengthy transcripts into compact, hierarchically structured codes and categories. We evaluate our method using extrinsic metrics aligned with human-assigned topic labels (ROUGE-L, cosine, BERTScore), and intrinsic metrics describing code groups (coverage, brevity, coherence, novelty, JSD divergence). Our results reveal a trade-off: density-based clustering achieves high coverage and strong cluster alignment, while direct LLM grouping results in higher fine-grained alignment, but lower coverage 20%. Overall, clustering maximizes coverage and structural separation, whereas LLM grouping produces more concise, interpretable, and semantically aligned categories. To support future research, we publicly release the full dataset of utterances and codes, enabling reproducibility and comparative studies.