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The phrase "a further subdivision" is correct and usable in written English.
It can be used when discussing categories or divisions within a larger classification, indicating an additional level of detail or separation.
Example: "In our analysis, we identified a further subdivision of the data that revealed interesting trends."
Alternatives: "an additional division" or "a subsequent category".
Exact(28)
And within that large category of arguments there is a further subdivision, about whether the methods of science can discover or distinguish that purpose.
Among the Jews there is a further subdivision of residential districts among ultraorthodox, traditional, and secular Jews, and Armenian Christians likewise form their own enclave in the Old City.
While he was alive, Shinran classified the existing schools of Buddhism into the schools of transcendence, which promises swift results and schools that are departing which require lengthy practice with a further subdivision of lengthwise and crosswise.
For the latter type a further subdivision can be made into spinal, brainstem, and cortical evoked potentials, according to the (assumed) structures from which the responses derive.
Furthermore, and as alluded to above, within the doxastic conception of probability we can make a further subdivision into subjective and objective doxastic attitudes.
There is a further subdivision for the use of catheterisation, shown by the payment of 1.66 for vignette 2 and 5 compared to 1.43 for vignette 3. The lower payment of 1.01 for vignette 6 is driven by its short length of stay, showing an outlier adjustment.
Similar(32)
Using both datasets, Rootstocks grouped clearly in a distinct cluster (Rs) with a possible further subdivision into two subgroups.
For N. concolor, our data indicate a separation of N. concolor lu from the remaining subspecies, which form a clade without further subdivision into taxa.
In a Dutch colon cancer study, further subdivision of comorbidity according to a modified Charlson classification did not improve the interpretation of comorbidity data (Lemmens et al, 2005).
These analyses subdivided the isolates into three previously recognized major lineages (A, B, and C), with further subdivision into 12 clonal sub-lineages or sub-groups and, finally, 221 unique MLVA15 genotypes.
A more restrictive definition and further subdivision of the current T3SE-families could improve the classification.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com