Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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 | #126×C127 | C2 |
| hypercenter | #126 | D127 |
| hypocenter | C127 | #563 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16861209 | C2 | semidirect |
| 2. #16861208 | C2 | semidirect |
| 3. #16861204 | C2 | semidirect |
| 4. #16861203 | C2 | semidirect |
| 5. #16861202 | C2 | semidirect |
| 6. #16861200 | C2 | semidirect |
| 7. #16861199 | C2 | semidirect |
| 11. #16861189 | C2 | semidirect |
| 12. #16861187 | C2 | semidirect |
| 13. #16861186 | C2 | semidirect |
| 14. #16861186 | C2 | semidirect |
| 15. #126×C127 | C2 | semidirect |
| 97. C127 | #563 | semidirect |
| 104. #126 | D127 | semidirect |