Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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 | C22⋊Q8×C127 | C2 |
| hypercenter | C22⋊Q8 | D127 |
| hypocenter | C127 | #536 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×D127 | C2 | semidirect |
| 3. #16861208 | C2 | semidirect |
| 4. #16861195 | C2 | semidirect |
| 5. #16861194 | C2 | semidirect |
| 6. #16861191 | C2 | semidirect |
| 7. #16861189 | C2 | semidirect |
| 8. #16861188 | C2 | semidirect |
| 9. #16861185 | C2 | semidirect |
| 10. #16861167 | C2 | semidirect |
| 11. C22⋊Q8×C127 | C2 | semidirect |
| 83. C127 | #536 | semidirect |
| 94. C22⋊Q8 | D127 | semidirect |