Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 111 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 | #120×C127 | C2 |
| hypercenter | #120 | D127 |
| hypocenter | C127 | #525 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14523247 | C2 | semidirect |
| 2. C23×Dic127 | C2 | semidirect |
| 3. #16861193 | C2 | semidirect |
| 4. #16861190 | C2 | semidirect |
| 5. #16861186 | C2 | semidirect |
| 6. #16861181 | C2 | semidirect |
| 7. #16861178 | C2 | semidirect |
| 8. D4×Dic127 | C2 | semidirect |
| 9. (C22⋊D127)⋊C4 | C2 | semidirect |
| 10. #16861165 | C2 | semidirect |
| 11. #120×C127 | C2 | semidirect |
| 13. C2×Dic254 | C22 | semidirect |
| 16. C2×C22⋊D127 | C22 | semidirect |
| 22. C22×Dic127 | C22 | semidirect |
| 23. C2×C4×D127 | C22 | semidirect |
| 24. C4⋊Dic127 | C22 | semidirect |
| 25. Dic127⋊C4 | C22 | semidirect |
| 26. Dic127⋊C4 | C22 | semidirect |
| 29. C22⋊Dic127 | C22 | semidirect |
| 30. (C2×D127)⋊C4 | C22 | semidirect |
| 31. C4×Dic127 | C22 | semidirect |
| 46. C2×Dic127 | D4 | semidirect |
| 69. C22×C127 | #41 | semidirect |
| 86. C127 | #525 | semidirect |
| 95. #120 | D127 | semidirect |
| 158. C22 | #14523247 | semidirect |