Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
310 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 111 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⋊Q8×C127 | C2 |
| hypercenter | C4⋊Q8 | D127 |
| hypocenter | C127 | #532 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14523249 | C2 | semidirect |
| 2. #16861206 | C2 | semidirect |
| 3. #16861198 | C2 | semidirect |
| 4. #16861184 | C2 | semidirect |
| 5. #16861171 | C2 | semidirect |
| 6. C42×D127 | C2 | semidirect |
| 7. C4⋊Q8×C127 | C2 | semidirect |
| 30. C4×D127 | D4 | semidirect |
| 42. C4×C127 | #41 | semidirect |
| 49. C127 | #532 | semidirect |
| 52. C4⋊Q8 | D127 | semidirect |
| 94. C4 | #14523249 | semidirect |