Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D127 |
| commutator, socle | C22×C127 | C24 |
| Fitting | #121×C127 | C2 |
| hypercenter | #121 | D127 |
| hypocenter | C127 | #546 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14523248 | C2 | semidirect |
| 2. C2×D4×D127 | C2 | semidirect |
| 3. #16861196 | C2 | semidirect |
| 4. #16861191 | C2 | semidirect |
| 5. #16861189 | C2 | semidirect |
| 6. #16861180 | C2 | semidirect |
| 7. #16861177 | C2 | semidirect |
| 8. #16861171 | C2 | semidirect |
| 9. C4×C22⋊D127 | C2 | semidirect |
| 10. C22⋊C4×D127 | C2 | semidirect |
| 11. #121×C127 | C2 | semidirect |
| 14. C2×Dic254 | C22 | semidirect |
| 18. C2×C22⋊D127 | C22 | semidirect |
| 21. C2×C4×D127 | C22 | semidirect |
| 22. C2×C4×D127 | C22 | semidirect |
| 23. C4⋊Dic127 | C22 | semidirect |
| 24. Dic127⋊C4 | C22 | semidirect |
| 25. C22⋊Dic127 | C22 | semidirect |
| 26. C22⋊Dic127 | C22 | semidirect |
| 27. C22⋊Dic127 | C22 | semidirect |
| 30. (C2×D127)⋊C4 | C22 | semidirect |
| 31. C4×Dic127 | C22 | semidirect |
| 33. C2×D4×C127 | C22 | semidirect |
| 34. C22×C4×C127 | C22 | semidirect |
| 35. C4⋊C4×C127 | C22 | semidirect |
| 36. C22⋊C4×C127 | C22 | semidirect |
| 43. D508 | D4 | semidirect |
| 75. C2×D127 | #41 | semidirect |
| 90. C127 | #546 | semidirect |
| 98. #121 | D127 | semidirect |
| 112. C2×D4 | C2×D127 | semidirect |
| 116. C22×C4 | C2×D127 | semidirect |
| 119. C4⋊C4 | C2×D127 | semidirect |
| 126. C22⋊C4 | C2×D127 | semidirect |