A good project manager is a good facilitator. Someone who can guide healthy conversations and help the team get to, remember and follow through on their commitments and decisions.
Taking a people focus I'd advise two key areas:
1- Who does what, by when: At the very basic, that's all project management is, tracking who is doing what and when it should be done. We often get wrapped up in the big ticket items of a release (new database, new UI, new web store) that we don't track the smaller things. As Tobias referenced, your team is probably still in the Storming phase. This is a time when you need to be tracking even the little things. So keep a simple action item and decision log. During any meeting, just jot down a capital A- for any action and a D- for anything decided. Dump this into a simple spreadsheet and share it through the preferred method.
2- Understand how your team wants to be communicated to: Peter Drucker's communication principles have been paraphrased as "Communication is what the listener does." If someone isn't being communicated to in the way they understand, then often they won't get it and even worse, they'll clam up and not communicate back.
I've found the DISC profile system incredibly simple and effective in helping me get a team communicating better. In a hyper nutshell DISC has four main quadrants:
"D"- Direct and to the point. No problem interrupting or being interrupted. Hates long stories or any explanation that starts with "Well..."
"I"- The influencer. Like Tom Sawyer, he'll get the job done most likely by getting everyone else involved. Highly distractable and can talk about pretty much nothing for hours.
"S" - The team mom. They want nothing more than everyone to get along and the work to get done. They won't confront and will rarely speak up in a large group.
"C" - The data person. There is no such thing as too much data and why explain something in ten words when a ten page email will do. Doesn't like to be surprised and will take their time to formulate an answer.
None of these is good or bad and the best teams have a healthy mix of all these types (and hybrid types like High D/I or High D/C). The important thing to note though is that the "D" and "I" people do not have a problem speaking up and can be very "forceful" in meetings. Two "D"s can seem like they are fighting when they are just communicating in their element.
Understanding your team, you can then work with them. In those large meetings, temper the "D" and "I"s a bit by asking for the "C" and "S" to contribute. If you know some major discussions are going to be happening, give the "C" and "S" a heads up so they have time to research or work out their thoughts. For the "D" keep things short and simple. You take the time to read the "C"'s 12 page report and summarize it in the meeting.
Learning how your team communicates and then setting up an environment where everyone gets heard, will solve a lot of the "Storming" issues your team is having.