President Carter has given Washington a new kind of undercover power politics. It's called government reorganization.

It's a subterranean game that mostly bores the general public, but is played with deadly seriousness by the movers and shakers in the bureaucracy and the city's big interest groups.

What they realize that the rest of us don't is that government reorganization has little to do with efficiency or moving boxes around on charts: it's really a battle over political power and turf.

Take, for example, the fight over reorganizing the government's education programs -- a fight that President Carter has decided, according to administration sources, should be resolved by creating a new Cabinet-level Department of Education.

The National Education Association, the nation's largest teacher organization, and most elementary and secondary school lobby groups are all for it.So are the junior colleges. They all think it will increase their political clout, and bring more federal dollars flowing their way.

But the American Federation of Teachers is dead set against it -- at least in part because arch-rival NEA is for it. So is the AFL-CIO, which fears a new department would include some of the training programs in the Department of Labor where it now swings a heavy stick.

Colleges and university lobbyists are lukewarm to the idea. They're afraid it will give too much power to the NEA and its allies. That translates into less money for them.

To make matters worse, the Carter administration is split over a depart ment. Both Carter and Vice President Mondale endorsed the idea during their election campaigns. Health, Education and Welfare Secretary Joseph A. Califano Jr., however, has a longstanding public position against it. "The joke around here is that Califano is like Lyndon Johnson in Vietnam: he doesn't want to go down in history as the first HEW secretary to lose a war," said one official on califano's policy staff.

With the President's Reorganization Project working on 31 different reorganizational efforts, involving huge chunks of the bureaucracy, the prospects of similar "wars" are almost limitless.

In almost every case to date, "the turf issues have been the most emotional," says Pat Gwaltney, who leads the group looking into education and human services reorganization. "We're talking about shifting power.

If you give more power to governors, mayors and communities, you take power away from someone else. That makes people nervous."

When environmental groups heard that thought was being given to folding the Environmental Protection Agency into a proposed new Department of Natural Resources, they hit the roof. The EPA has been their special baby.

"The cost of reorganization in terms of confusion and lost momentum is very hihg," a statement signed by the Conservation Foundation and 26 other groups declared.

But some of the same groups split over a less ambitious plan to remove a multimillion-dollar water treatment grant program from the EPA and put it into a new Natural Resources Department. That's because some of them already have cozy relations with the Interior Department, which would form the nucleus of the new department.

Sydney Howe, executive director of the Urban Environmental Conference, was outraged. He spelled out the power politics behind it this way:

"If the treatment grants were removed from EPA, the big losers would be the progressive environmental movement and the urban and public health constituencies it increasingly embraces. . . Leaders and representatives of local governments, health organizations and environmental groups have established working and lobbying relationships with the agency's influential regional offices. They might be left searching for attention on treatment requirements if the grants program were placed under a Natural Resources Department."

The heavies in the Interior Department would love getting water pollution control in their hands, he added. "The new Department of Energy has drawn important functions away from Interior, which could well be looking for appropriate replacements. The huge treatment grants program in EPA would seem an attractive candidate."

But no reorganization project has caused quite as much handwringing as the proposed new Department of Education, an idea that has been floating around at least since 1922.

There's a basic logic to it. The federal government administers 256 educational programs, scattered in 40 agencies. HEW alone shells out more than $10 billion a year on education --an amount larger than the budgets of five existing departments -- Interior, Commerce, Justice, State and Energy. The Departments of Agriculture and Defense are also into education in a big way.

A handful of congressmen and senators have been introducing bills to create a separate department for years. But the issue has never been the type to stir deep emitions. "It's not the kind of issue that a politician is willing to bleed and die on," says one lobbyist.

This time it's different. Carter endorsed a department in his campaign, and 57 senators co-sponsored a bill calling for a department. The President's Reorganization Project began a study of it last summer. On Nov. 28, it presented its finding to the President, Mondale, Califano and the President's top political and domestic aides in a lengthy, impassioned meeting.

It was during this session that Carter made it clear he still favored a broad-based new Department of Education and Human Development -- one of three options presented, according to administration spokesmen.

Just what kind of department remains in doubt. Carter has yet to make a public statement on it, although Califano said Wednesday that Carter intends to deliver a special education message to Congress before Feb. 15 in which he presumably would spell out his plans. In addition, there is widespread speculation that he may make some mention of it in his State of the Union address on Thursday.

Then the battle will break into the open. Educational groups say it will turn on what is included in a new department.

The indications are the administration favors a broad-based Department of Education and Human Development. This, sources indicate in interviews, could mean taking the Job Corps and some other training programs from the Labor Department, nutrition and school lunch programs from the Agriculture Department, juvenile delinquency programs from Justice. The Bureau of Indian Affairs from the Interior Department, and most educational and human development programs -- such as Head Start and drug abuse -- programs out of HEW.

The trouble is that each agency has a constituency and friends in Congress. Many have congressional subcommittees assigned to oversee them with no other reason for being. Any realignment of agencies would cause a realignment in power bases on Capitol Hill. That kind of talk sends congressmen into a cold sweat.

"Politically, the narrower the department is the better off we are" says NEA lobbyist Stanley MacFarland.

The Reorganization Project has already gotten a taste of what this means. When it briefed lobbyists from the National Association of Counties and other groups on its tentative plans, for instance, several lobbyists jumped all over them.

"We told them the plan was naive. We told them special-interest groups would eat them alive on the Hill," recalls one lobbyist present. "They're dividing everyone's constituency."