Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
330 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D127 |
| commutator | C2×C127 | C23×C4 |
| Frattini | C22 | C23×D127 |
| Fitting | C2×C4⋊C4×C127 | C2 |
| socle | C23×C127 | C23 |
| hypercenter | C2×C4⋊C4 | D127 |
| hypocenter | C127 | C2×#117 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16861167 | C2 | direct (N × H) |
| 3. C2×C4⋊Dic127 | C2 | semidirect |
| 5. C2×C4×Dic127 | C2 | semidirect |
| 6. C2×C4⋊C4×C127 | C2 | semidirect |
| 10. C2×C4×D127 | C4 | semidirect |
| 12. C4⋊Dic127 | C22 | semidirect |
| 14. C4×Dic127 | C22 | semidirect |
| 17. C4⋊C4×C127 | C22 | semidirect |
| 26. C4×D127 | C2×C4 | semidirect |
| 44. C2×C127 | #117 | semidirect |
| 49. C127 | C2×#117 | semidirect |
| 54. C2×C4⋊C4 | D127 | semidirect |
| 65. C4⋊C4 | C2×D127 | semidirect |
| 95. C2 | #16861167 | direct (N × H) |