Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 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 | C2 | C2×D4×D127 |
| commutator | C4×C127 | C24 |
| Frattini | C4 | C23×D127 |
| Fitting | #137×C127 | C2 |
| socle | C2×C127 | C22×D4 |
| hypercenter | #137 | D127 |
| hypocenter | C127 | #578 |
| LCS | G ▷ C4×C127 ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #137 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16861257 | C2 | semidirect |
| 2. #16861256 | C2 | semidirect |
| 3. #16861242 | C2 | semidirect |
| 4. #16861241 | C2 | semidirect |
| 5. #16861238 | C2 | semidirect |
| 6. #16861230 | C2 | semidirect |
| 7. #16861229 | C2 | semidirect |
| 8. C2×#14523238 | C2 | semidirect |
| 9. Q16×D127 | C2 | semidirect |
| 10. #16861217 | C2 | semidirect |
| 11. #137×C127 | C2 | semidirect |
| 87. C127 | #578 | semidirect |
| 94. #137 | D127 | semidirect |