Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
334 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 115 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 | C22×D4×C89 | C2 |
| hypercenter | C22×D4 | D89 |
| hypocenter | C89 | #546 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13083573 | C2 | semidirect |
| 2. #15667999 | C2 | semidirect |
| 3. #15667993 | C2 | semidirect |
| 4. #15667991 | C2 | semidirect |
| 5. #15667984 | C2 | semidirect |
| 6. #15667983 | C2 | semidirect |
| 7. #15667981 | C2 | semidirect |
| 8. D4×Dic89 | C2 | semidirect |
| 9. C4×C22⋊D89 | C2 | semidirect |
| 10. C2×C22⋊Dic89 | C2 | semidirect |
| 11. C22×D4×C89 | C2 | semidirect |
| 13. C2×Dic178 | C22 | semidirect |
| 15. C2×C22⋊D89 | C22 | semidirect |
| 16. C2×C22⋊D89 | C22 | semidirect |
| 17. C22×Dic89 | C22 | semidirect |
| 18. C22×Dic89 | C22 | semidirect |
| 19. C2×C4×D89 | C22 | semidirect |
| 20. C4⋊Dic89 | C22 | semidirect |
| 21. #13083553 | C22 | semidirect |
| 22. #13083553 | C22 | semidirect |
| 25. C22⋊Dic89 | C22 | semidirect |
| 26. C22⋊Dic89 | C22 | semidirect |
| 27. C22⋊Dic89 | C22 | semidirect |
| 28. C22⋊Dic89 | C22 | semidirect |
| 29. #13083551 | C22 | semidirect |
| 30. C4×Dic89 | C22 | semidirect |
| 46. D4×C89 | D4 | semidirect |
| 71. C22×C89 | #41 | semidirect |
| 90. C89 | #546 | semidirect |
| 93. C22×D4 | D89 | semidirect |
| 141. D4 | C22⋊D89 | semidirect |
| 165. C22 | #13083573 | semidirect |