Groupings? HELP!!!

[Baylian]

I took my CZ 550 .270 Win. to the range today. It is grouping weird. With some types of ammo I get 2 shots close (under .75 inch) together and then the 3rd shot is off (usually low and to the right) making a 1.5 inch or worse group. If I put a fourth into this group it usually hits close to one of the 2 close holes. The Nosler Partition and Grand Slam formed a 1.75 inch triangle. Nosler Accubonds string out wide (3+inches) from 8:30 to 2:30. I don't think my CZ likes Accubonds. Last time at the range it was a 5.5 inch group. I really wanted to shoot this cartridge at elk. SST's have a vertical string at about less than 1.5 inches. A couple other ammo types strung out 11 to 5. Can anyone give me some suggestions to improve the accuracy of my rifle? The range master checked and the barrel is free floated. I was using a Caldwell sand bag as a rest and a sand bag under the butt. This is all factory ammo. I don't reload (yet). The target that accompanied the rifle when I bought it had a ragged .6 inch hole for a 5 shot group at 50 m.

Thanks in advance, TJ