Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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 | #127×C127 | C2 |
| hypercenter | #127 | D127 |
| hypocenter | C127 | #535 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14523247 | C2 | semidirect |
| 2. C2×D4×D127 | C2 | semidirect |
| 3. #16861205 | C2 | semidirect |
| 4. #16861197 | C2 | semidirect |
| 5. #16861196 | C2 | semidirect |
| 6. #16861181 | C2 | semidirect |
| 7. #16861177 | C2 | semidirect |
| 8. #16861166 | C2 | semidirect |
| 9. #127×C127 | C2 | semidirect |
| 12. C2×Dic254 | C22 | semidirect |
| 16. C2×C22⋊D127 | C22 | semidirect |
| 18. C22×Dic127 | C22 | semidirect |
| 20. Dic127⋊C4 | C22 | semidirect |
| 21. C22⋊Dic127 | C22 | semidirect |
| 23. (C2×D127)⋊C4 | C22 | semidirect |
| 24. C4×Dic127 | C22 | semidirect |
| 26. C2×D4×C127 | C22 | semidirect |
| 27. C2×D4×C127 | C22 | semidirect |
| 28. C42×C127 | C22 | semidirect |
| 42. C4×D127 | D4 | semidirect |
| 71. C127 | #535 | semidirect |
| 76. #127 | D127 | semidirect |
| 91. C2×D4 | C2×D127 | semidirect |
| 92. C2×D4 | C2×D127 | semidirect |
| 100. C42 | C2×D127 | semidirect |