Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
346 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 346 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×D89 |
| commutator, socle | C22×C89 | C24 |
| Fitting | #121×C89 | C2 |
| hypercenter | #121 | D89 |
| hypocenter | C89 | #534 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×D89 | C2 | semidirect |
| 2. #15667997 | C2 | semidirect |
| 3. #15667994 | C2 | semidirect |
| 4. #15667986 | C2 | semidirect |
| 5. #15667984 | C2 | semidirect |
| 6. #15667982 | C2 | semidirect |
| 7. #15667980 | C2 | semidirect |
| 8. C2×#13083551 | C2 | semidirect |
| 9. #121×C89 | C2 | semidirect |
| 11. C23×D89 | C22 | semidirect |
| 13. C2×D356 | C22 | semidirect |
| 15. C2×C22⋊D89 | C22 | semidirect |
| 16. C2×C22⋊D89 | C22 | semidirect |
| 18. C22×Dic89 | C22 | semidirect |
| 19. C2×C4×D89 | C22 | semidirect |
| 20. C4⋊Dic89 | C22 | semidirect |
| 21. #13083553 | C22 | semidirect |
| 22. C22⋊Dic89 | C22 | semidirect |
| 23. #13083551 | C22 | semidirect |
| 24. #13083551 | C22 | semidirect |
| 25. #13083551 | C22 | semidirect |
| 26. #13083551 | C22 | semidirect |
| 27. C2×D4×C89 | C22 | semidirect |
| 28. C2×D4×C89 | C22 | semidirect |
| 29. C22×C4×C89 | C22 | semidirect |
| 30. C4⋊C4×C89 | C22 | semidirect |
| 31. C22⋊C4×C89 | C22 | semidirect |
| 39. C22×D89 | D4 | semidirect |
| 84. C89 | #534 | semidirect |
| 91. #121 | D89 | semidirect |
| 103. C2×D4 | C2×D89 | semidirect |
| 104. C2×D4 | C2×D89 | semidirect |
| 107. C22×C4 | C2×D89 | semidirect |
| 110. C4⋊C4 | C2×D89 | semidirect |
| 116. C22⋊C4 | C2×D89 | semidirect |