Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 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 | C22 | C23×D127 |
| commutator, socle | C22×C127 | C24 |
| Fitting | #124×C127 | C2 |
| hypercenter | #124 | D127 |
| hypocenter | C127 | #529 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16861202 | C2 | semidirect |
| 2. #16861201 | C2 | semidirect |
| 3. #16861191 | C2 | semidirect |
| 4. #16861185 | C2 | semidirect |
| 6. Q8×Dic127 | C2 | semidirect |
| 7. D4×Dic127 | C2 | semidirect |
| 8. (C22⋊D127)⋊C4 | C2 | semidirect |
| 9. #16861165 | C2 | semidirect |
| 10. C42×D127 | C2 | semidirect |
| 11. #124×C127 | C2 | semidirect |
| 74. C127 | #529 | semidirect |
| 78. #124 | D127 | semidirect |