Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
228 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D127 |
| commutator, socle | C22×C127 | C24 |
| Fitting | C4×D4×C127 | C2 |
| hypercenter | C4×D4 | D127 |
| hypocenter | C127 | #554 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16861208 | C2 | semidirect |
| 2. #16861201 | C2 | semidirect |
| 3. #16861200 | C2 | semidirect |
| 4. #16861188 | C2 | semidirect |
| 5. #16861186 | C2 | semidirect |
| 6. #16861186 | C2 | semidirect |
| 7. C4×Dic254 | C2 | semidirect |
| 10. C2×Dic127⋊C4 | C2 | semidirect |
| 46. D4×C127 | Q8 | semidirect |
| 70. C127 | #554 | semidirect |
| 109. D4 | Dic254 | semidirect |