Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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. #26014957 | C2 | semidirect |
| 4. #26014915 | C2 | semidirect |
| 6. C8×Dic353 | C2 | semidirect |
| 7. #106×C353 | C2 | semidirect |
| 11. #19150726 | C4 | semidirect |
| 22. Dic706 | C2×C4 | semidirect |
| 33. C8×C353 | C2×C4 | semidirect |
| 44. Dic353 | SD16 | semidirect |
| 49. C353 | C4×SD16 | semidirect |
| 54. #106 | D353 | semidirect |
| 83. C8 | C4×D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150726 | 2 |
| #26014957 | 2 |
| #26014954 | 2 |
| #26014915 | 2 |
| #26014912 | 2 |
| C8×Dic353 | 2 |
| #106×C353 | 2 |
| C4×SD16 | 353 |