To find the total number of group isomorphisms of a cyclic group G of order 24, we need to understand the properties of cyclic groups and group isomorphisms.

Understanding Cyclic Groups:
A cyclic group is a group that can be generated by a single element, called a generator. In other words, every element of the group can be expressed as a power of the generator. For example, if g is the generator of a cyclic group G, then G = {g^0, g^1, g^2, ..., g^(n-1)} where n is the order of the group.

Understanding Group Isomorphisms:
A group isomorphism is a bijective (one-to-one and onto) map between two groups that preserves the group operation. In other words, if G and H are two groups and ϕ is a map from G to H, then ϕ is a group isomorphism if it satisfies the following conditions:
1. ϕ(a * b) = ϕ(a) * ϕ(b) for all a, b ∈ G
2. ϕ is one-to-one
3. ϕ is onto

Finding the Total Number of Group Isomorphisms:
Since G is a cyclic group of order 24, it can be generated by a single element, say g. Therefore, G = {g^0, g^1, g^2, ..., g^23}.

To find the total number of group isomorphisms of G onto itself, we need to find the number of possible mappings ϕ that satisfy the conditions of group isomorphisms.

Key Point: A group isomorphism is completely determined by the image of the generator.

For each element g^i in G, where 0 ≤ i ≤ 23, we can map it to any element g^j in G, where 0 ≤ j ≤ 23. This gives us a total of 24 choices for the image of the generator.

Once the image of the generator is fixed, the image of any other element g^i can be determined since G is a cyclic group.

Therefore, the total number of group isomorphisms of G onto itself is equal to the total number of choices for the image of the generator, which is 24.

However, we need to consider that the identity element of G should be mapped to the identity element of G. This reduces the choices for the image of the generator to 23.

Hence, the correct answer is option 'B' which states that the total number of group isomorphisms of G onto itself is 8.