Maybe I'm a member of too many groups on LinkedIn (I am a member of 31 groups), but from the profiles I see every day, being a member to, say, over 15-20 groups is not that unusual. While I am a member of many groups, there are about 2-3 that I participate in and about 5-6 others that I pay attention to for marketing/industry intelligence purposes. The others I check in with as appropriate. Therefore, the default alphabetical listing of the groups has always frustrated me. I'm not frustrated anymore because I found the answer.
You can specify the display order of your groups. Let's walk through how to do it.
Under your name at the top right, choose Settings
Choose the tab "Groups, Companies & Applications"
Under "Groups," choose the first item, "Select your group display order"
You'll see a page with your groups listed in alpha order. Reordering is cumbersome from here but doable. Decide which group you would like to appear at the top of your list and then click that up arrow next to the numbered box. HINT: this up arrow moves the group to the #1 spot, not just up one notch. From here, choose which group you would like to appear second and place a 2 in the box, and so on. Depending on the number of groups you belong to, you might have to play with it a while but it does work. You see here a few of my groups and their order.
Another useful tool is the option to display between 1 and 10 groups in the navigation on your page. I've chosen 6 as you can see here.
After you're finished, hit Save.
Then, from when you click the "Groups" menu item, you'll see the groups as you ordered them. Remember, I chose to see only the first 6 and here they are.
So, that's how you do it. I hope this was helpful to you. If you have any LinkedIn hints, let me know.