Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 63 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, socle | C23×C127 | C23 |
| Fitting | C2×C22⋊C4×C127 | C2 |
| hypercenter | C2×C22⋊C4 | D127 |
| hypocenter | C127 | #393 |
| LCS | G ▷ C23×C127 ▷ C127 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic254 | C2 | semidirect |
| 3. C127⋊#95 | C2 | semidirect |
| 4. C127⋊#95 | C2 | semidirect |
| 26. C23×C127 | Q8 | semidirect |
| 52. C127 | #393 | semidirect |
| 72. C23 | Dic254 | semidirect |