Omega’s (famous) 19’’’ pocket watch was introduced in 1894 (together with similar movements of different sizes within the ‘family’). The 19’’’CHRO was introduced in 1898 and added the chronograph complication.
There were many variations of both dial and case. It was produced as both lépine (open face) and savonette (hunter)(for the savonette, the button under the bow was used to open the cover, the chrono functions were carried out with a separate pusher at 6 o’clock.
The choice of case material included almost everything (gold, silver, niello, nickel, steel - both blackened or gun metal, etc). The quality of movement varied (the better grades having jewelled chrono mechanisms - see image below).
The chrono minutes sub-dial (at 12 o’clock) was either 15 or 30 minutes (see images). A special ‘Cadran s.g.d.g.’ dial (image below) was (usually) fitted to a larger version of the same movement (19/22’’’) - the same movement mounted in a spacer - and this (usually) had only one sub-dial, a 15-minute chrono at 12 o’clock . There were still more (tachymetric and telemetric) dial versions.
Ringed in an image below is the ‘finger piece’, mounted on the chronograph wheel, which turned the chrono minute hand exactly on the elapsed minute (as opposed to the minute hand moving continuously).
As we see in the images, the OP’s watch was the original 19’’’ CHRO version, with a 15‑minute sub-dial and a continuous seconds sub-dial at 6 o’clock. All grades (of the version the OP shows) had a swan-neck regulator.
The 19’’’ CHRO was followed (1906) by the 18’’’P CHRO (also both lépine and savonette). ‘P’ stood for the French ‘Plat’, meaning flat (because the movement was only 7.15 mm thick, compared with the 9.25 mm of the 19’’’ CHRO. In 1929 came the 39 CHRO (only lépine). In 1932 (after Lemania had joined) came the wrist chronographs (28.9 in 1932, 33.3 in 1933) and then in 1942 the 27 CHRO - which led on to the 321 and …. yes, the Speedmaster!