Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 334 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×D353 |
| commutator, socle, cosocle | C22×C353 | C24 |
| Fitting | #121×C353 | C2 |
| hypercenter | #121 | D353 |
| hypocenter | C353 | #535 |
| LCS | G ▷ C22×C353 ▷ C353 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19150737 | C2 | semidirect |
| 2. C2×D4×D353 | C2 | semidirect |
| 3. #26014988 | C2 | semidirect |
| 4. #26014978 | C2 | semidirect |
| 5. #26014967 | C2 | semidirect |
| 6. #26014966 | C2 | semidirect |
| 7. #26014963 | C2 | semidirect |
| 8. #26014962 | C2 | semidirect |
| 9. #26014960 | C2 | semidirect |
| 10. #26014950 | C2 | semidirect |
| 11. #121×C353 | C2 | semidirect |
| 14. C2×Dic706 | C22 | semidirect |
| 17. C2×D1412 | C22 | semidirect |
| 20. C2×C22⋊D353 | C22 | semidirect |
| 21. C2×C22⋊D353 | C22 | semidirect |
| 22. C2×C22⋊D353 | C22 | semidirect |
| 25. C2×C4×D353 | C22 | semidirect |
| 26. C4⋊Dic353 | C22 | semidirect |
| 27. C22⋊Dic353 | C22 | semidirect |
| 29. #19150714 | C22 | semidirect |
| 30. #19150714 | C22 | semidirect |
| 31. C4×Dic353 | C22 | semidirect |
| 33. C2×D4×C353 | C22 | semidirect |
| 34. C22×C4×C353 | C22 | semidirect |
| 35. C4⋊C4×C353 | C22 | semidirect |
| 36. C22⋊C4×C353 | C22 | semidirect |
| 56. C4×D353 | D4 | semidirect |
| 96. C353 | #535 | semidirect |
| 105. #121 | D353 | semidirect |
| 122. C2×D4 | C2×D353 | semidirect |
| 125. C22×C4 | C2×D353 | semidirect |
| 127. C4⋊C4 | C2×D353 | semidirect |
| 132. C22⋊C4 | C2×D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150737 | 2 |
| C2×D4×D353 | 2 |
| #26014988 | 2 |
| #26014978 | 2 |
| #26014967 | 2 |
| #26014966 | 2 |
| #26014963 | 2 |
| #26014962 | 2 |
| #26014960 | 2 |
| #26014950 | 2 |
| #121×C353 | 2 |
| #535 | 353 |