22 is the maximum number of sixes hit in a one day innings, done by New Zealand against West Indies. This was the match in which Corey Anderson broke record of fastest century, off 36 balls, hitting 14 sixes alone while Jesse Ryder contributed 5 and Brendon McCullum 3.
That match broke the record set by India and Australia when both teams had hit 19 sixes each in that ODI at Bangalore. Rohit Sharma had made 209, second highest score in the format, smashing 16 sixes while Glenn Maxwell hit 7, James Faulkner 6, Shane Watson 6, MS Dhoni 1 and Yuvraj Singh 1.
Recently, West Indies became only other team to hit 19 sixes in an inning, against Bangladesh as Denesh Ramdin hit 11 and Darren Bravo 8. Together, those two added 258 runs which is highest partnership for West Indies in the format, ever.
There have been 4 other occasions when a team hit 18 sixes in their inning, and 6 times 16 sixes.
Most sixes by a team in a one day international
22 sixes = New Zealand vs West Indies at Q'town, 22 fours, 1 Jan 2014.
19 sixes = India vs Australia at Bengaluru, 30 fours, 2 Nov 2013.
19 sixes = Australia vs India at Bengaluru, 29 fours, 2 Nov 2014.
19 sixes = West Indies vs Bangladesh at St Kitts, 19 fours, 25 Aug 2014.
18 sixes = South Africa vs Holland at Basseterre, 30 fours, 16 Mar 2007.
18 sixes = India vs Bermuda at Port of Spain, 30 fours, 19 March 2007.
18 sixes = New Zealand vs Ireland at Aberdeen, 28 fours, 1 July 2008.
18 sixes = India vs New Zealand at Christchurch, 32 fours, 8 March 2009.