So, even though I worked there for almost 5 years I had to do a little research to try and understand how HP is currently organized. I put together the graphic below. Until 2014, I worked in IPG (Imaging and Printing Group) that is now a part of the Printing and Personal Systems Group. HP is currently organized into 4 (formerly 7) business units that each operate internationally.
Each top-level business unit has an executive vice president that sits on the company's board of directors. Each business unit also has a VP for each geographic region. Those business units are additionally broken into down into product groups or lab groups (read: R&D) with their own VPs that manage the development and manufacturing of products. Teams within product groups for specific products dissolve quickly after the product has been put into production, but those team members usually stay within their product group.
This organizational structure lends itself to deep expertise in product development (see: printers) that is efficient and leverages the existing supply and manufacturing chains very efficiently (strength). However, in an environment where synergy creates innovation, it's a disadvantage that business units are often separated onto different HP sites and are organizationally discouraged from interacting (weakness).
Even though HP is separated into business units, there are a number of functional units that are managed across the organization. Though staff in each functional unit report to a functional-unit vice president, employees are often assigned to a primary product group (e.g. a marketing professional will report to the marketing VP, but will also work with the printers group). Certainly, this is cost effective and creates economies of scale for hiring, ad buys, client management and litigation. Functional units include HR, marketing, business development and legal.
In the coming year, HP is splitting into two publicly traded companies. The first will house printing and personal systems (all hardware). The other will house the other three business units (software and services). Hopefully, HP will use this as an opportunity to create synergy between software and service BUs and develop new products and revenue models that better utilize HP's expertise (opportunity). HP's Printing and Personal Systems unit is currently the largest revenue generator, but it is also the most threatened unit because of declining print sales and lack of innovation (threat and weakness respectively). Apple pioneered the model of developing software in conjunction with hardware and HP has chosen to adopt the opposite model.
While working at HP, I helped develop a new consumer print service without the expertise of marketing, help from legal or perspectives from regional leaders until we were many years along in development. Today's best executed products learn and fail quickly. HP has made this almost impossible by shielding new businesses from the entire organization until they are "ready" for primetime. If this is repeated across all business units (and now two separate publicly traded companies) this will be a major disadvantage for HP.