Looking on the internet deeply has found these results:

I suggest you to contact them is the most popular phrase on the web.

I suggest you contacting them 12,530 results on the web	I suggest you to contact them 1137,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
I suggest you stop questioning my authority. I suggest you two leave Colombia. I suggest you interview her first. I suggest you start locking your doors. The Commission suggests contacting the abovementioned Agency for further information concerning implementation of the programme in Romania. As regards any official languages for the event, therefore, the Commission would suggest contacting the organisers, namely Unesco, the Spanish State, the Generalitat de Catalunya and the Ajuntament de Barcelona. I suggest you leave right now. And I suggest you reconsider that statement.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

I suggest you contacting them

12,530 results on the web

I suggest you to contact them

1137,000 results on the web

More popular!

I suggest you stop questioning my authority.
I suggest you two leave Colombia.
I suggest you interview her first.
I suggest you start locking your doors.
The Commission suggests contacting the abovementioned Agency for further information concerning implementation of the programme in Romania.
As regards any official languages for the event, therefore, the Commission would suggest contacting the organisers, namely Unesco, the Spanish State, the Generalitat de Catalunya and the Ajuntament de Barcelona.
I suggest you leave right now.
And I suggest you reconsider that statement.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.