MySQL sorting by date with GROUP BY
===

My table `titles` looks like this

    id |group|date                |title
    ---+-----+--------------------+--------
    1  |1    |2012-07-26 18:59:30 | Title 1
    2  |1    |2012-07-26 19:01:20 | Title 2
    3  |2    |2012-07-26 19:18:15 | Title 3
    4  |2    |2012-07-26 20:09:28 | Title 4
    5  |2    |2012-07-26 23:59:52 | Title 5

I need latest result from each group ordered by date in descending order. Something like this

    id |group|date                |title
    ---+-----+--------------------+--------
    5  |2    |2012-07-26 23:59:52 | Title 5
    2  |1    |2012-07-26 19:01:20 | Title 2

I tried

    SELECT *
    FROM `titles`
    GROUP BY `group`
    ORDER BY MAX( `date` ) DESC

but I'm geting first results from groups. Like this

    id |group|date                |title
    ---+-----+--------------------+--------
    3  |2    |2012-07-26 18:59:30 | Title 3
    1  |1    |2012-07-26 19:18:15 | Title 1

What am I doing wrong?
Is this query going to be more complicated if I use LEFT JOIN?