Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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×D89 |
| commutator, socle | C22×C89 | C24 |
| Fitting | C2×C22⋊C4×C89 | C2 |
| hypercenter | C2×C22⋊C4 | D89 |
| hypocenter | C89 | #551 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15668005 | C2 | semidirect |
| 2. #15668005 | C2 | semidirect |
| 3. #15667998 | C2 | semidirect |
| 4. #15667996 | C2 | semidirect |
| 5. #15667995 | C2 | semidirect |
| 6. #15667994 | C2 | semidirect |
| 7. #15667991 | C2 | semidirect |
| 8. #15667989 | C2 | semidirect |
| 10. C4×C22⋊D89 | C2 | semidirect |
| 11. #15667972 | C2 | semidirect |
| 12. #15667971 | C2 | semidirect |
| 13. #15667968 | C2 | semidirect |
| 14. C2×C22⋊Dic89 | C2 | semidirect |
| 15. C2×C22⋊C4×C89 | C2 | semidirect |
| 16. C2×Dic178 | C22 | semidirect |
| 22. C2×C4×D89 | C22 | semidirect |
| 23. C4⋊Dic89 | C22 | semidirect |
| 24. C4⋊Dic89 | C22 | semidirect |
| 25. C4⋊Dic89 | C22 | semidirect |
| 26. #13083553 | C22 | semidirect |
| 27. #13083553 | C22 | semidirect |
| 28. #13083553 | C22 | semidirect |
| 29. #13083553 | C22 | semidirect |
| 30. #13083553 | C22 | semidirect |
| 38. #13083551 | C22 | semidirect |
| 39. #13083551 | C22 | semidirect |
| 40. #13083551 | C22 | semidirect |
| 41. C4×Dic89 | C22 | semidirect |
| 42. C4×Dic89 | C22 | semidirect |
| 43. C4×Dic89 | C22 | semidirect |
| 110. C89 | #551 | semidirect |
| 126. C2×C22⋊C4 | D89 | semidirect |