How to get user security group name through javascript

if you are working on SharePoint 2013 Version, then it is easy to get current user groupcollection through rest api in javascript.

script would be like this :

 function getCurrentUserGroupColl(UserID)
 {
  $.ajax
  ({
  url: "/sites/dev/_api/web/GetUserById("+UserID+")/Groups",
  type: "GET",
  headers: { "Accept": "application/json; odata=verbose","X-RequestDigest": $("#__REQUESTDIGEST").val() },
  dataType: "json",
  async: true,
   success: function(data){
      /* get all group's title of current user. */
      var results = data.d.results;
      for(var i=0; i< results.length; i++)
      {
            console.log(results[i].Title)
      }
  }
  });
}


function getCurrentUser()
{
 $.ajax
  ({
  url: "/sites/dev/_api/web/CurrentUser",
  type: "GET",
  headers: { "Accept": "application/json; odata=verbose","X-RequestDigest": $("#__REQUESTDIGEST").val() },
  dataType: "json",
  async: true,
  success: function(data){
    getCurrentUserGroupColl(data.d.Id)
  }
  });
}  

$(document).ready(function(){ getCurrentUser();  });

Hope it helps!!

You can try this code snippet to target your functionality through ECMA script:

var adminUsers;
var vCurrUserName;
var groupCollection;
var _group;

function checkUser() {
var currentContext = new SP.ClientContext.get_current();

//get current user

vCurrUserName = currentContext.get_web().get_currentUser();

currentContext.load(vCurrUserName);

// get Admin group

groupCollection = currentContext.get_web().get_siteGroups();
currentContext.load(groupCollection);

//var _group = groupCollection.getById(10); // ID of the Group

currentContext.executeQueryAsync(Function.createDelegate(this, this.checkUserSuccess),
  Function.createDelegate(this, this.checkUserFailure));

}
var vIsAdmin = false;
function checkUserSuccess() {
var currentContext = new SP.ClientContext.get_current();

var grpEnum = groupCollection.getEnumerator();

while(grpEnum.moveNext()){
var grpItem = grpEnum.get_current();
currentContext.load(grpItem);

// here you can add one more if condition to check for "Approvers" group.

if(grpItem.get_title() == "Member"){
    _group = grpItem;
    break;
 }
}

adminUsers = _group.get_users();
currentContext.load(adminUsers);

currentContext.executeQueryAsync(Function.createDelegate(this, this.findUserInGroup), 
Function.createDelegate(this, this.checkUserFailure));
}

function findUserInGroup(){
var listEnumerator = adminUsers.getEnumerator();

while (listEnumerator.moveNext()) {

var item = listEnumerator.get_current();

//check current user login name and user login name from admin group

if (vCurrUserName.get_loginName() == item.get_loginName()) {

vIsAdmin = true;

break;

    }

}

if (vIsAdmin) {
  // do something here
}
else
{
  // do something here
}