That is a woody compound umbel. A compound umbel is one with more than one set of pedicels) between the peduncle) and the flower. Hydrangeas also exhibit this type of inflorescence, although not necessarily woody.
In the picture below, I've marked all the levels where the pedicels branch.
1. End of peduncle, beginning of primary pedicels
2. Beginning of secondary pedicels
3. Beginning of tertiary pedicels
4. Beginning of quaternary pedicels, which bear flowers
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