Here's the list, in groups of seven, as some translations have it:
1 Jesus - Joseph - Heli - Matthat - Levi - Melchi - Janna
2 Joseph - Mattathiah - Amos - Nahum - Esli - Naggai - Maath
3 Mattathiah - Semei - Joseph - Judah - Joannas - Rhesa - Zerubbabel
4 Shealtiel - Neri - Melchi - Addi - Cosam - Elmodam - Er
5 Jose - Eliezer - Jorim - Matthat - Levi - Simeon - Judah
6 Joseph - Jonan - Eliakim - Melea - Menan - Mattathah - Nathan
7 David - Jesse - Obed - Boaz - Salmon - Nahshon - Amminadab
8 [Admin] - Ram - Hezron - Perez - Judah - Jacob - Isaac
9 Abraham Terah - Nahor - Serug - Reu - Peleg - Eber
10 Shelah - [Cainan] - Arphaxad - Shem - Noah - Lamech - Methuselah
11 Enoch - Jared - Mahalalel - Cainan - Enosh - Seth - Adam
"Admin" in group 8, is not well attested by Greek manuscripts. Some translations choose to include him, and some don't. In the words of Metzger, "Faced with a bewildering variety of readings, the Committee adopted what seems to be the least unsatisfactory form of the text".
"Cainan" in group 10 is better attested by manuscripts, though some early manuscripts do not include him. However, it is more likely that the name "Cainan" was added than that it was removed - it would be very easy for a copyist copying a list of weird names to accidentally copy the same name twice (cf its undisputed occurrence in group 11).
Another argument against the inclusion of these two names is that the author of Luke knew the Old Testament well - it is difficult to see how he might have screwed up the genealogies between David and Adam, as these are easily found in Chronicles, and partially also Genesis (though "Cainan" is found in the LXX, though it was probably added either by a series of mistakes, or intentionally to create a 7+7+7+etc. symmetry - this was probably incorporated later into Luke by copyists). Albeit, though less likely, it is possible that the changes went the other way.
In short, I think it is likely that the author of Luke intended to chronicle the actual genealogy of Jesus, and that later copyists added a couple of names to make the genealogy fit well in groups of seven, and possibly also to make the genealogy fit the Septuagint's genealogy in Gen 11. These groups of seven probably are not intended have any symbolic value per se, but rather make the genealogy look "pretty" by making it into parallel groups with a "biblical" number. It is unlikely that the genealogy was manufactured to have more prominent people at the beginning of each group - the Old Testament chronology already has Enoch seven generations from Adam, and the modifications to Luke's chronology bring only two prominent people (3 with Jesus) to the beginning of groups - and do so by placing a fictitious person at the beginning of a group (#8, Admin). The duplication of names at the beginning of groups is not significant, as it would be even weirder if the beginning of groups did not duplicate names - many names are repeated often in this list (Jesus x2, Joseph x3, Matthat x2, Levi x2, Mattathiah x2 (in addition to Matthat and Mattathah), Judah x2).