JSFiddle - React, Tailwind, and code Playground

HTML

<div id="t"></div>

JavaScript

var dates = [1367848800000, 1367935200000, 1368021600000,
           1368108000000, 1368194400000, 1368367200000,
           1368540000000, 1368626400000, 1368712800000];

var k = 0 , 
   sorted = [];   

sorted[k] = [];

dates.sort( function ( a, b ){

    return +a > +b ? 1 : +a == +b ? 0: -1;
})
.forEach( function( v , i ){
    var a = v,b = dates[i+1]||0;
    
    sorted[k].push( +a );
    
    if ( (+b - +a) > 86400000) {
            sorted[++k] = []
    }
    return 1;
});
 
sorted.sort( function ( a,b ){
    return a.length > b.length ? -1: 1;
});

document.getElementById('t').innerHTML = sorted.join('<br />');