So, normally, a group in normal walk can cover 36 km a day. How much can a group on horseback or any similar mount cover? The PHB really doesn't help with this.

It's in the DMG and Basic Rules.

Travel Pace

While traveling, a group of adventurers can move at a normal, fast, or slow pace, as shown on the Travel Pace table. The table states how far the party can move in a period of time and whether the pace has any effect. A fast pace makes characters less perceptive, while a slow pace makes it possible to sneak around and to search an area more carefully.

Forced March. The Travel Pace table assumes that characters travel for 8 hours in day. They can push on beyond that limit, at the risk of exhaustion.

For each additional hour of travel beyond 8 hours, the characters cover the distance shown in the Hour column for their pace, and each character must make a Constitution saving throw at the end of the hour. The DC is 10 + 1 for each hour past 8 hours. On a failed saving throw, a character suffers one level of exhaustion.

Mounts and Vehicles. For short spans of time (up to an hour), many animals move much faster than humanoids. A mounted character can ride at a gallop for about an hour, covering twice the usual distance for a fast pace. If fresh mounts are available every 8 to 10 miles, characters can cover larger distances at this pace, but this is very rare except in densely populated areas.

Characters in wagons, carriages, or other land vehicles choose a pace as normal. Characters in a waterborne vessel are limited to the speed of the vessel, and they don't suffer penalties for a fast pace or gain benefits from a slow pace. Depending on the vessel and the size of the crew, ships might be able to travel for up to 24 hours per day.

Certain special mounts, such as a pegasus or griffon, or special vehicles, such as a  broom of flying, allow you to travel more swiftly.

Pace	Distance per Minute	Distance per Hour	Distance per day	Effect
Fast	400 feet	4 miles	30 miles	-5 penalty to passive Wisdom (Perception) scores
Normal	300 feet	3 miles	24 miles	-
Slow	200 feet	2 miles	18 miles	Able to use stealth

Difficult Terrain

The travel speeds given in the Travel Pace table assume relatively simple terrain: roads, open plains, or clear dungeon corridors. But adventurers often face dense forests, deep swamps, rubble-filled ruins, steep mountains, and ice-covered ground--all considered difficult terrain.

You move at half speed in difficult terrain--moving 1 foot in difficult terrain costs 2 feet of speed--so you can cover only half the normal distance in a minute, an hour, or a day.