Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D127 |
| commutator | C2×C127 | C2×C42 |
| Frattini | C23 | C22×D127 |
| Fitting | C2×C42×C127 | C2 |
| socle | C23×C127 | C23 |
| hypercenter | C2×C42 | D127 |
| hypocenter | C127 | C4×C22⋊C4 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C4×Dic127 | C2 | semidirect |
| 4. C127⋊#95 | C2 | semidirect |
| 5. C2×C42×C127 | C2 | semidirect |
| 11. C2×C4×D127 | C4 | semidirect |
| 12. (C2×D127)⋊C4 | C4 | direct (N × H) |
| 27. C2×Dic127 | C2×C4 | semidirect |
| 33. C2×C4×C127 | C2×C4 | semidirect |
| 45. C2×D127 | C42 | semidirect |
| 47. C4×C127 | C22⋊C4 | semidirect |
| 56. C127 | C4×C22⋊C4 | semidirect |
| 61. C2×C42 | D127 | semidirect |
| 90. C2×C4 | C4×D127 | semidirect |
| 106. C4 | (C2×D127)⋊C4 | direct (N × H) |