Not exactly sure that I follow your requirements, but it sounds like you could use UNION to combine two data sets, one with a GROUP BY and one without. You're not including any aggregate logic in your select, so I assume that in this instance you're using GROUP BY to achieve the same effect as DISTINCT and avoid repeated rows in the non-private list of meetings (??).

SELECT

[DATE],

[TypeofMeeting],

[NameofMeeting]

FROM

dbo.meetings

WHERE

[TypeofMeeting] = 'private'

UNION ALL

SELECT

[DATE],

[TypeofMeeting],

[NameofMeeting]

FROM

dbo.meetings

WHERE

[TypeofMeeting] <> 'private'

GROUP BY

[DATE],

[TypeofMeeting],

[NameofMeeting]