Republic of Singapore Navy, since 1967
The naval and government ensigns of Singapore both have a cool 8-pointed star motif in the lower right corner. I’m not sure if it represents anything specifically. Maybe just the standard compass rose/navigation sort of thing?
Before the navy was split off as its own thing in 1975, this was the flag of the Maritime Command of the Singapore Armed Forces.
Singapore Army (?-Present)
The Army of Singapore has a cool yellow ensign, with the Army’s badge all the away down in the lower right corner. The interesting thing about this ensign is that the flag in the top left corner isn’t the flag of Singapore, but rather the top left corner of the flag of Singapore.
September 16 is Malaysia Day, the date when Singapore, Sabah, and Sarawak united with the Federation of Malaya to form the new state of Malaysia. Malaya’s flag was very similar to the current flag of Malaysia, except it had eleven stripes and an eleven-pointed star, representing the 11 states of the federation.
The fourteenth point and stripe on the current flag were retained even after Singapore became an independent country in 1965. They’re now said to represent the Federal Territories.
Singapore owes its flag to a bit of good old fashioned Cold War hysteria. In the original proposal it was supposed to have three stars and an all-red background, but the Malayan Communist Party also used three stars (representing Malays, Indians, and Chinese) and the colour red had obvious communist connections. The white stripe and two extra stars were added to assuage these symbolic concerns.