The extracellular or intracellular nature of biodegradation majorly depends on the trans-membrane transport of the concerned pollutant. The trans-membrane transport of any molecule depends on the size of the molecule and its charge or chemical nature of it.
1,4 dioxane has a relatively smaller molecular size and is chemically classified as an ether. Thus, it is expected that 1,4 dioxane must be transported into the cell; hence, the bio-degradation could be intracellular.
But in certain cases, things always do not follow certain rules. Sometimes chemical contaminants could increase oxidoreductive stress to the microbial community, stimulating secretions of different oxidoreductase enzymes. This also resulted in the degradation of such pollutants. Hence to some extent, it could be concluded as the extracellular or intracellular nature of biodegradation not only depends on the type of the contaminant but also on the ability or potential of the biodegradation agent.