Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
330 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D127 |
| commutator, socle | C22×C127 | C24 |
| Frattini | C22 | C23×D127 |
| Fitting | #117×C127 | C2 |
| hypercenter | #117 | D127 |
| hypocenter | C127 | #525 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14523248 | C2 | semidirect |
| 2. C22×C4×D127 | C2 | semidirect |
| 3. #16861193 | C2 | semidirect |
| 4. #16861189 | C2 | semidirect |
| 5. #16861184 | C2 | semidirect |
| 6. #16861179 | C2 | semidirect |
| 7. C4×D508 | C2 | semidirect |
| 8. #117×C127 | C2 | semidirect |
| 11. C2×Dic254 | C22 | semidirect |
| 13. C2×D508 | C22 | semidirect |
| 19. C2×C4×D127 | C22 | semidirect |
| 20. C4⋊Dic127 | C22 | semidirect |
| 22. (C2×D127)⋊C4 | C22 | semidirect |
| 24. C4⋊C4×C127 | C22 | semidirect |
| 26. C42×C127 | C22 | semidirect |
| 42. C2×C4×C127 | D4 | semidirect |
| 54. C2×D127 | #41 | semidirect |
| 65. C127 | #525 | semidirect |
| 74. #117 | D127 | semidirect |
| 88. C4⋊C4 | C2×D127 | semidirect |
| 92. C42 | C2×D127 | semidirect |
| 108. C2×C4 | D508 | semidirect |