Before the merger: Vodafone Group plc owned Vodafone Australia...

Before the merger:
Vodafone Group plc owned Vodafone Australia Limited (which runs the Vodafone network)
Hutchison Whampoa Limited owned 52% of Hutchison Telecommunications (Australia) Limited ("HTAL"), which owned Hutchison 3G Australia Pty Limited ("H3GA") (which runs the "3" network)

In the merger, Hutchison 3G Australia was renamed Vodafone Hutchison Australia Pty Ltd, and 50% was sold to Vodafone Group.

The ownership structure of the merged entity became:
Vodafone Group owns 50% of Vodafone Hutchison Australia Pty Ltd
Hutchison Telecommunications Australia owns 50% of Vodafone Hutchison Australia Pty Ltd
Vodafone Hutchison Australia Pty Ltd owns 100% of Vodafone Australia Limited[12]