under or beneath that.
under the authority of or in accordance with that.

before 900; Middle English therunder, Old English thǣrunder. See there, under Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
thereunder (ˌðɛərˈʌndə)
1.  (in documents, etc) below that or it; subsequently in that; thereafter
2.  under the terms or authority of that

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

O.E. þærunder; see there + under.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
They wore turbans too, and thereunder peered out their elfin faces at me,-faces
  with protruding lower-jaws and bright eyes.
These certificates are arranged chronologically by year and thereunder by month.
Thereunder these four are arranged either alphabetically by unit name or
  numerically by unit number.
By community, thereunder by plat, thereunder by block.
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