Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D127 |
| commutator | C22×C127 | C22×C4 |
| Fitting | C2×C4⋊C4×C127 | C2 |
| socle | C23×C127 | C23 |
| hypercenter | C2×C4⋊C4 | D127 |
| hypocenter | C127 | #385 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Dic127⋊C4 | C2 | semidirect |
| 5. C127⋊#95 | C2 | semidirect |
| 6. C127⋊#95 | C2 | semidirect |
| 7. C2×C4⋊C4×C127 | C2 | semidirect |
| 17. (C2×D127)⋊C4 | C4 | semidirect |
| 36. C2×Dic127 | C2×C4 | semidirect |
| 47. C2×C4×C127 | C2×C4 | semidirect |
| 62. C2×D127 | C4⋊C4 | semidirect |
| 77. C127 | #385 | semidirect |
| 81. C2×C4⋊C4 | D127 | semidirect |
| 125. C2×C4 | C4×D127 | semidirect |