Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D127 |
| commutator, socle | C22×C127 | C22×C4 |
| Fitting | C2×M16×C127 | C2 |
| hypercenter | C2×M16 | D127 |
| hypocenter | C127 | #435 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C8×D127 | C2 | semidirect |
| 3. Dic127⋊C8 | C2 | semidirect |
| 4. C22⋊(C127⋊C8) | C2 | semidirect |
| 5. (C2×D127)⋊C8 | C2 | semidirect |
| 6. #16861119 | C2 | semidirect |
| 7. C2×M16×C127 | C2 | semidirect |
| 36. C8×C127 | D4 | semidirect |
| 43. C2×D127 | M16 | semidirect |
| 55. C127 | #435 | semidirect |
| 57. C2×M16 | D127 | semidirect |
| 92. C8 | C22⋊D127 | semidirect |