Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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 | #123×C353 | C2 |
| hypercenter | #123 | D353 |
| hypocenter | C353 | #525 |
| LCS | G ▷ C22×C353 ▷ C353 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19150736 | C2 | semidirect |
| 2. C22×C4×D353 | C2 | semidirect |
| 3. #26014975 | C2 | semidirect |
| 4. #26014970 | C2 | semidirect |
| 5. #26014965 | C2 | semidirect |
| 6. #26014962 | C2 | semidirect |
| 7. #26014960 | C2 | semidirect |
| 8. #26014954 | C2 | semidirect |
| 9. #26014952 | C2 | semidirect |
| 10. #26014948 | C2 | semidirect |
| 11. #123×C353 | C2 | semidirect |
| 14. C2×Dic706 | C22 | semidirect |
| 18. C2×C22⋊D353 | C22 | semidirect |
| 20. C22×Dic353 | C22 | semidirect |
| 24. C2×C4×D353 | C22 | semidirect |
| 25. #19150716 | C22 | semidirect |
| 26. #19150716 | C22 | semidirect |
| 30. #19150714 | C22 | semidirect |
| 31. C4×Dic353 | C22 | semidirect |
| 34. C4⋊C4×C353 | C22 | semidirect |
| 36. C22⋊C4×C353 | C22 | semidirect |
| 47. C2×Dic353 | D4 | semidirect |
| 72. C2×D353 | #41 | semidirect |
| 86. C353 | #525 | semidirect |
| 91. #123 | D353 | semidirect |
| 116. C4⋊C4 | C2×D353 | semidirect |
| 122. 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×#19150736 | 2 |
| C22×C4×D353 | 2 |
| #26014975 | 2 |
| #26014970 | 2 |
| #26014965 | 2 |
| #26014962 | 2 |
| #26014960 | 2 |
| #26014954 | 2 |
| #26014952 | 2 |
| #26014948 | 2 |
| #123×C353 | 2 |
| #525 | 353 |