【Large】 , 【big】 ,  【great】  mean above the average of its kind in magnitude, especially physical magnitude.

【Large】 may be preferred when the dimensions, or extent, or capacity, or quantity, or amount is being considered.

【Big】 , on the other hand, is especially appropriate when the emphasis is on bulk, or mass, or weight, or volume.

As applied to material objects,  【great】  has been practically displaced by  【large】  or  【big】 . Where  【great】 is used to denote physical magnitude, it now regularly connotes some impression (as of wonder, surprise, amusement, or annoyance) associated with the size.

【Great】 alone, in standard English, expresses degree. In extended use,  【great】 suggests eminence, distinction, or supremacy while  【large】 suggests breadth, comprehensiveness, or generosity and  【big】 carries over the implication of mass or bulk but often suggests impressiveness or importance rather than solidity or 【great】 worth.