FGB Holding Corp., the new owner of Financial General Bankshares Inc., plans a capital injection of $12 million in the Washington-based bank holding company.

The new capital funds will strengthen the company's subsidiary banks and "permit them to offer broadened and improved services in their respective markets," top executives of FGB said.

That much has been disclosed in this year's Financial General annual report. But little else is known of FGB's plans for Financial General and its 12 subsidiary banks, including the three First American Banks in the Washington area.

FGB officials say they will be prepared to disclose the company's plans in greater detail after Financial General's annual meeting, which is scheduled for late July or early August.

The Middle Eastern investors, who spent more than $200 million in acquiring Financial General in a tender offer two months ago, have said repeatedly during the past four years that under new management, the subsidiary banks will develop new growth opportunities and become more competitive.

In fact, plans and strategies are already being developed, FGB's top executives stated recently. Those plans will produce "exciting" changes, promised one.

Shortly after the investors indicated their interest in acquiring Financial General more than four years ago, it became clear why a $2 billion company with 12 small banks appealed to them. It is "uniquely positioned," say FGB officials, to take advantage of dramatic changes that are expected in the banking industry.

Indeed, compared with other multibank holding companies, Financial General is uniquely positioned with subsidiary banks in the District, Maryland, Virginia, Tennessee and New York. And the new owners are counting heavily on a presence in Washington and New York for the development of a strong international banking operation.

As a first step, FGB will change the corporate name of its subsidiary from Financial General Bankshares to First American Bankshares, creating a stronger identity with its banks in this area. It's possible that the names of other subsidiary banks may be changed to establish the new corporate identity.

It's also possible, say banking sources, that five smaller subsidiary banks throughout Virginia will be merged into Financial General's First American Bank in McLean. Such a merger would also solve an identity problem and provide a more coordinated banking operation in Virginia.

The same sources say the owners of First American Bankshares will probably try to extend the company's presence in Maryland to include the major Baltimore market after strengthening its base here and in New York.

From all indications, however, the next major change will involve a more centralized administrative structure in which subsidiary banks will no longer operate independently of each other.

Financial General's previous management was criticized often for its lack of aggressiveness in coordinating the development of its banks in key markets.

At one point the new owners cited "a paucity of leadership" at Financial General that prevented it from realizing "its full potential for growth and performance."

The combined average net income of Financial General banks increased about 16 percent from 1976 through the end of last year and combined assets increased only 8 percent.

Of all the Financial General banks, only First American of Virginia, the biggest of the group, with assets of more than $900 million, has exhibited an aggressive growth posture in that span.

Under the new ownership structure, FGB Chairman Clark M. Clifford and President Robert G. Stevens wrote recently, there are "substantial prospects for the development of important banking opportunities, both domestically and internationally."

By coordinating the banks' activities in the new holding company, the new owners suggested some time ago, they could become important institutions in serving the U.S. banking needs of Middle Eastern customers as well as providing financing for U.S. customers doing business in the Middle East.

The new owners believe they can achieve their goals best by operating as a privately held company.

As such, it will probably be the only multibank corporation of its size in the United States to remain private.

"There are any number of advantages to being privately held," an FGB official replied when asked about the decision to go private.

For one thing, control of the Financial General banks by a relatively small group of investors will give them freedom to implement business decisions without the bother of stockholder concerns or refusal to go along with controversial management proposals.