Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #123×C89 | C2 |
| hypercenter | #123 | D89 |
| hypocenter | C89 | #538 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15668007 | C2 | semidirect |
| 2. #15668005 | C2 | semidirect |
| 3. #15667998 | C2 | semidirect |
| 4. #15667998 | C2 | semidirect |
| 5. #15667997 | C2 | semidirect |
| 6. #15667992 | C2 | semidirect |
| 7. #15667986 | C2 | semidirect |
| 8. #15667985 | C2 | semidirect |
| 9. #15667983 | C2 | semidirect |
| 10. #15667982 | C2 | semidirect |
| 11. #15667980 | C2 | semidirect |
| 12. #15667974 | C2 | semidirect |
| 13. C4×C22⋊D89 | C2 | semidirect |
| 14. C22⋊C4×D89 | C2 | semidirect |
| 15. #123×C89 | C2 | semidirect |
| 17. C2×Dic178 | C22 | semidirect |
| 23. C2×C22⋊D89 | C22 | semidirect |
| 26. C2×C4×D89 | C22 | semidirect |
| 27. C4⋊Dic89 | C22 | semidirect |
| 28. C4⋊Dic89 | C22 | semidirect |
| 29. #13083553 | C22 | semidirect |
| 30. #13083553 | C22 | semidirect |
| 33. C22⋊Dic89 | C22 | semidirect |
| 40. #13083551 | C22 | semidirect |
| 41. #13083551 | C22 | semidirect |
| 42. C4×Dic89 | C22 | semidirect |
| 43. C4×Dic89 | C22 | semidirect |
| 45. C22×C4×C89 | C22 | semidirect |
| 46. C4⋊C4×C89 | C22 | semidirect |
| 47. C4⋊C4×C89 | C22 | semidirect |
| 50. C22⋊C4×C89 | C22 | semidirect |
| 116. C89 | #538 | semidirect |
| 123. #123 | D89 | semidirect |
| 145. C22×C4 | C2×D89 | semidirect |
| 150. C4⋊C4 | C2×D89 | semidirect |
| 151. C4⋊C4 | C2×D89 | semidirect |
| 165. C22⋊C4 | C2×D89 | semidirect |