Anything that is underexposed in any camera will have a noise issue. I'd like to see a 100% crop of the wall that is at the top. I would guess it is completely noise free. However what you are looking at is a very underexposed shadow. I would also venture a guess that you have the Auto Lighting Optimizer on and are shooting in jpeg. The optimizer will automatically brighten shadows for you-causing more noise problems.
The area you have cropped to is a pretty harsh shadow you are in there, so I am guessing that in post processing you are keeping that mid-tone shadow fairly high or even brightening/adding exposure to it.
You never want to underexpose anything at any ISO. When you are setting exposure you should be setting it to the point JUST below where something would blow out that you can't have happen. Don't forget that if you are using the highlight warnings to tell you where you have a blow out it will highlight if ONE color channel is blown. Often times one color being blown is proper. In the case of your green wall you may find that it registers the red channel blown if you raised exposure properly on it. SO, make sure you are thinking a bout that blinking highlight warning and what it's telling you too.
Your exposure on this one if this is SOOC could go up probably close to 2 stops in exposure.
When you reduce exposure a little or add black in post processing you help to hide or even eliminate noise. If you bump brightness at all you are running the risk of adding noise.
One more thing-I have heard arguments for and against the in-between ISO's. I have heard that they can be a headache as they aren't TRUE ISO's, but the camera boosting to the in between step, and I have heard the opposite as well. I have never bothered to test it myself. I always slightly over expose and have never had cause think there is any problem with those in-betweens.
Full ISO's (in case someone doesn't know) are 100, 200, 400, 800, 1600, 3200, 6400, 12800