Mention Motorola and most people think cell phones. But if speculation that the company might say goodbye to its phone business proves true, Motorola will lose its core brand.

What would a Razr-less Motorola do? While its best known for phones, which account for about two-thirds of revenues, the embattled company has two other big business units: Enterprise mobility, which sells radios to the government, and home and networks mobility, which makes cellular infrastructure equipment and cable set-top boxes, among other products. And unlike its cell phone unit — which last quarter incurred an operating loss of $138 million — some of these other businesses are actually showing strong growth.

That’s why some analysts (and activist investor Carl Icahn) argue that hanging up on the cell phone business could benefit Motorola (MOT) shareholders. Case in point: While phones sales were down 36 percent last quarter compared to the previous year, sales of home and networks mobility products were up 6 percent and the enterprise mobility solutions business was up 47 percent.

“Motorola does have a leadership position in several markets,” notes Lawrence Harris, an analyst with Oppenheimer & Co.

Of course, not all of Motorola’s secondary businesses are booming. Ping Zhao, a senior analyst with CreditSights, says sales of cellular infrastructure equipment are in an industry-wide slump. Still, she puts Motorola’s total value without its handset business, at about $29 billion.

“Without the handsets you’ve got some businesses that are very interesting and very strong,” says Zhao. “Basically, the sum of its parts is greater than than its stock price would suggest.” Though Zhao says breaking up the company would be advantageous from a shareholder’s perspective, she adds that it’s not clear what it would mean for Motorola in the long run.

Motorola declined to comment on whether it would consider selling off its phone division.

Icahn recently claimed that doing so would produce almost $20 billion of additional shareholder value. The company’s third-largest shareholder has been pushing to split up the company since the Razr started its downward spiral. Former CEO Ed Zander opposed Icahn’s plan but new chief executive Greg Brown may be more amenable to making changes.

“While I do think the new CEO is going to take the opportunity to review the company’s portfolio, I would be surprised if we were to see significant action in the near term,” says Harris, the Oppenheimer & Co. analyst.

One of the reasons Motorola might be reluctant to sell its mobile devices unit, says Harris, is that it has synergies with other businesses within the company, such as cellular infrastructure equipment.

But last week acting Motorola finance chief Tom Meredith opened the door slightly by telling a group of investors that while Motorola could remain intact, “A change in circumstance sometimes requires a change in action. So I will leave it at that.”

Changing circumstances are the nature of the wireless market. Just two years ago, everyone wanted to own a super-thin Razr. But then competitors caught up with the clamshell phone while Apple (AAPL), Nokia (NOK) and other phonemakers started coming out with multimedia devices that left Motorola in the dust.

Of course, the company founded in 1928 as a manufacturer of in-car radios and other products has played a key role in the development of cell phones and has bounced back before. If the handset business stays with the company, it’s not impossible the phonemaker could regain its former glory.