Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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 | C2×C22⋊C4×C127 | C2 |
| hypercenter | C2×C22⋊C4 | D127 |
| hypocenter | C127 | #538 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16861202 | C2 | semidirect |
| 2. #16861195 | C2 | semidirect |
| 3. #16861191 | C2 | semidirect |
| 4. #16861188 | C2 | semidirect |
| 5. #16861183 | C2 | semidirect |
| 6. #16861182 | C2 | semidirect |
| 7. #16861178 | C2 | semidirect |
| 8. C4×C22⋊D127 | C2 | semidirect |
| 9. C2×C22⋊C4×C127 | C2 | semidirect |
| 10. C2×Dic254 | C22 | semidirect |
| 11. C2×D508 | C22 | semidirect |
| 15. C2×C4×D127 | C22 | semidirect |
| 16. C4⋊Dic127 | C22 | semidirect |
| 17. C4⋊Dic127 | C22 | semidirect |
| 18. Dic127⋊C4 | C22 | semidirect |
| 19. Dic127⋊C4 | C22 | semidirect |
| 23. (C2×D127)⋊C4 | C22 | semidirect |
| 24. (C2×D127)⋊C4 | C22 | semidirect |
| 25. C4×Dic127 | C22 | semidirect |
| 74. C127 | #538 | semidirect |
| 84. C2×C22⋊C4 | D127 | semidirect |