Barry Diller's leisure empire continues to grow. This morning's fourth-quarter report out of IAC/InterActiveCorp (NASDAQ:IACI) confirms that all four of the company's core businesses keep clawing their way to higher ground.

For the quarter itself, adjusted profits per share rose from $0.50 to $0.67. Analysts were expecting a $0.53-per-share showing. Revenue climbed 8% higher to hit $1.8 billion, just shy of Wall Street's target. Yes, the company's posted profits tanked, but that's what happens when you're a conglomerate sentenced to a lifetime of one-time charges.

When you're dealing with a colorful mosaic like IAC, it's probably best to take it one tile at a time. Let's do that by taking a peek at all four of the company's key areas.

Q4 Rev. Growth

Retailing

4%

Services

8%

Media and advertising

46%

Memberships and subscriptions

3%



Retailing
Retailing still makes up more than half of the company's revenue mix (54%). However, running the Home Shopping Network, a series of catalogs, and the Shoebuy online shoe store doesn't produce the same kind of attractive margins you'll find in the company's inventory-free Internet businesses. So despite its thick slice on the top line, retailing accounts for just a 36% chunk of IAC's operating profits before amortization costs.

Over at HSN, there was marginal growth despite the company's shift away from consumer electronics and into jewelry and accessories. Yes, everybody else seems to be selling a ton of electronic gadgetry these days, but that's also a good reason for HSN to go in a different direction to stand out. Despite the lower selling prices and higher return rate, the company was able to make it up in volume.

As for Shoebuy, 2007 is going to be an important year. Gap (NYSE:GPS) and Amazon.com (NASDAQ:AMZN) have launched stand-alone stores that specialize in the free delivery of high-end footwear. Psst, Shoebuy. Consumer electronics much?

Services
It was a mixed bag on the services side. Business was booming at Ticketmaster. Things also went well at ServiceMagic, as the contractor referral service probably benefited from the burst of the real estate bubble. With more folks resigned to staying in their existing digs, renovating that bathroom or tacking on an extra room makes practical sense. The site received a 44% spike in lead requests.

However, that same sudsy pop also put a dent in the company's Lending Tree and RealEstate.com sites.

Media and advertising
It's now been a year since IAC gave its Ask.com search engine a massive makeover. Apparently, it's working. This was the company's best-performing sector, fueled by more sponsored searches going through Ask.com at higher price points.

Ask will never be Google (NASDAQ:GOOG), but it doesn't have to be. As long as it holds up -- and that's never a given, as even the mighty Microsoft (NASDAQ:MSFT) has seen its search business market share shrink over the past year -- the paid-search growth trajectory will serve it well.

Citysearch also produced healthy year-over-year growth for IAC. In fact, the only real downer here was Ask.com UK. Think they're missing Jeeves much across the pond, do you?

Membership and subscriptions
There were gains in the company's online dating sites, like Match.com and Chemistry. The company also fared well with its travel properties (timeshare-swapping Interval International and campground reservation specialist ReserveAmerica).

The one sour note here was a dip in the company's discounting business, led by the diminished distribution of its "Entertainment Books" loaded with localized coupons.

Piecing it together
Despite its stock tickling new highs, IAC has been aggressively buying back shares. That's a good thing, especially if the company feels as if it can continue to bankroll its relentless appetite for acquisitions.

As far as mosaics go, IAC is an intriguing piece of artistry. Sure, some of the tiles could stand to be polished, but why quibble? Take a few steps back. Look at the big picture. Diller's snapshot works.

Gap and Amazon.com have been popular recommendations for Motley Fool Stock Advisor subscribers. Microsoft and Gap made the cut for Inside Value readers.

Longtime Fool contributor Rick Munarriz does not own shares in any of the companies mentioned in this story, though he has been a frequent freelance contributor to IAC's CitySearch. He is also part of the Rule Breakers newsletter research team, seeking out tomorrow's ultimate growth stocks a day early. The Fool has a disclosure policy.