Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D127 |
| commutator | C2×C127 | C2×C42 |
| Fitting | #95×C127 | C2 |
| socle | C23×C127 | C23 |
| hypercenter | #95 | D127 |
| hypocenter | C127 | C4×C22⋊C4 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C4×Dic127 | C2 | semidirect |
| 4. C127⋊#95 | C2 | semidirect |
| 5. #95×C127 | C2 | semidirect |
| 10. C2×C4×D127 | C4 | semidirect |
| 11. (C2×D127)⋊C4 | C4 | semidirect |
| 23. C2×Dic127 | C2×C4 | semidirect |
| 31. C2×C4×C127 | C2×C4 | semidirect |
| 41. C2×D127 | C42 | semidirect |
| 45. Dic127 | C22⋊C4 | semidirect |
| 52. C127 | C4×C22⋊C4 | semidirect |
| 58. #95 | D127 | semidirect |
| 84. C2×C4 | C4×D127 | semidirect |