Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 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 | C2×C127 | C23×C4 |
| Fitting | C4×D4×C127 | C2 |
| socle | C22×C127 | C24 |
| hypercenter | C4×D4 | D127 |
| hypocenter | C127 | #520 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×Dic254 | C2 | semidirect |
| 3. #16861174 | C2 | semidirect |
| 4. D4×Dic127 | C2 | semidirect |
| 5. C4×C22⋊D127 | C2 | semidirect |
| 6. (C22⋊D127)⋊C4 | C2 | semidirect |
| 7. #16861166 | C2 | semidirect |
| 8. #16861165 | C2 | semidirect |
| 9. C2×Dic127⋊C4 | C2 | semidirect |
| 10. C4⋊C4×D127 | C2 | semidirect |
| 11. C4×D4×C127 | C2 | semidirect |
| 12. #14523247 | C4 | semidirect |
| 37. Dic254 | C2×C4 | semidirect |
| 38. C22⋊D127 | C2×C4 | semidirect |
| 40. C2×Dic127 | C2×C4 | semidirect |
| 47. C4×D127 | C2×C4 | semidirect |
| 49. D4×C127 | C2×C4 | semidirect |
| 76. C127 | #520 | semidirect |
| 84. C4×D4 | D127 | semidirect |
| 117. D4 | C4×D127 | semidirect |