Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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 | C4×D4×C89 | C2 |
| hypercenter | C4×D4 | D89 |
| hypocenter | C89 | #546 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13083573 | C2 | semidirect |
| 2. C2×D4×D89 | C2 | semidirect |
| 3. #15668000 | C2 | semidirect |
| 4. #15667996 | C2 | semidirect |
| 5. #15667992 | C2 | semidirect |
| 6. #15667987 | C2 | semidirect |
| 7. #15667986 | C2 | semidirect |
| 8. #15667982 | C2 | semidirect |
| 9. C4×D356 | C2 | semidirect |
| 10. C2×#13083551 | C2 | semidirect |
| 11. C4×D4×C89 | C2 | semidirect |
| 14. C2×Dic178 | C22 | semidirect |
| 17. C2×D356 | C22 | semidirect |
| 19. C2×C22⋊D89 | C22 | semidirect |
| 21. C22×Dic89 | C22 | semidirect |
| 23. C2×C4×D89 | C22 | semidirect |
| 24. C4⋊Dic89 | C22 | semidirect |
| 25. C4⋊Dic89 | C22 | semidirect |
| 28. #13083551 | C22 | semidirect |
| 29. #13083551 | C22 | semidirect |
| 30. #13083551 | C22 | semidirect |
| 31. #13083551 | C22 | semidirect |
| 33. C22×C4×C89 | C22 | semidirect |
| 34. C4⋊C4×C89 | C22 | semidirect |
| 35. C22⋊C4×C89 | C22 | semidirect |
| 36. C42×C89 | C22 | semidirect |
| 44. D4×C89 | D4 | semidirect |
| 75. C2×D89 | #41 | semidirect |
| 90. C89 | #546 | semidirect |
| 101. C4×D4 | D89 | semidirect |
| 116. C22×C4 | C2×D89 | semidirect |
| 119. C4⋊C4 | C2×D89 | semidirect |
| 126. C22⋊C4 | C2×D89 | semidirect |
| 127. C42 | C2×D89 | semidirect |
| 141. D4 | D356 | semidirect |