There is no way to push SplitViewController. If you want to use it according to apple it needs to be the root view of your application.
There is a workaround for that though (not %100 gauranteed to be accepted by apple). You need to change the Root of your main Window in AppDelegate manually and animate it yourself.
Edit:
I found some code for changing the rootViewController
of the window:
AppDelegate delegate = [[UIApllication sharedApplication] delegate];
[[delegate window] rootViewController] = yourSplitViewController;