Help required in pushing of surfaces

I’m trying to extrude a portion of a hexagonal prism so that it looks like this.

Unfortunately, when I move the selected plane surface, undesirable morphing occurs.

hexagonal module.3dm (337.0 KB)

I made the desirable output by exporting the 3dm file to Sketchup and pushing the surfaces upwards.
How can I achieve the same in Rhino?

You can use direct editing on many Rhino geometries by holding control + shift and simultaneously clicking on a surface for example. Or select one surface after another, while holding control + shift

Use the gumball to scale with factor 0 to make it flat.

Use the gumball to move your geometry or parts of it to a certain height

Not sure if your bottom surface needs the division. You can get rid of it with the command MergeAllCoplanarFaces

If instead you just want a clean surface instead of the many isocurves, you can delete it and type cap to build a fresh surface.

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Moving the doodled faces while holding ctrl+shift gives warping. I want to have this type of geometry

Even in this photo warping is happening which is not required.

Select the 3 bottom faces and use ExtrudeSrf with the DeleteInput option set to Yes. Do not use the Gumball to do this.

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Sorry I was giving you instructions on how to fix the warped surface

Thanks! That worked!