Here's one way to do it:
-The washer drain goes vertically to a point a above the horizontal branch where you can get at least 18" of standpipe above the trap weir.
-The washer hose must connect to the standpipe via an "air break" so that waste, sump or sewage water cannot be siphoned back into the washing machine and potentially into your drinking supply.
-The standpipe drain must connect to the horizontal sump pump branch using a Wye as Glennjannie stated, or must connect directly to the vertical stack also using a Wye. Attaching to the vertical stack would eliminate any need for any check valves.
The point is that the washer has it's own internal 'check valve' so none is normally needed in the discharge hose. And because the washer must be connected via an air break, any water that backs up via the standpipe-horizontal branch connection is simply going to spill out onto the floor and not back into the washing machine.
You need to understand that an 'air break' is a an arrangement where a discharge pipe from an appliance, fuxture or device drains indirectly
into a receptor below
the flood level rim of the receptor but above
the trap seal.
In the case of a washing machine standpipe, the 'air break' is created thusly:
The washing machine pump only pumps the water to a point high enough that it can empty via gravity
into an standpipe, which is an air break type receptor.
In your diagram, the washing maching was pumping the waste water directly into a waste pipe connected to the drain.
This is a major non-no because backflow or backsiphonage in your case can cause polluted or contaminated water to get back inside the washer and potentially into the drinking supply system.