Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
106 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26014998 | C2 | semidirect |
| 3. #26014927 | C2 | semidirect |
| 4. #26014919 | C2 | semidirect |
| 5. #26014918 | C2 | semidirect |
| 6. C8×Dic353 | C2 | semidirect |
| 7. #131×C353 | C2 | semidirect |
| 9. #19150727 | C4 | semidirect |
| 10. #19150725 | C4 | semidirect |
| 11. #19150724 | C4 | semidirect |
| 12. #19150722 | C4 | semidirect |
| 51. C353 | #443 | semidirect |
| 55. #131 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26015012 | 2 |
| #26014998 | 2 |
| #26014927 | 2 |
| #26014919 | 2 |
| #26014918 | 2 |
| C8×Dic353 | 2 |
| #131×C353 | 2 |
| #443 | 353 |