Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
192 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. #26014990 | C2 | semidirect |
| 4. #26014983 | C2 | semidirect |
| 5. #26014983 | C2 | semidirect |
| 6. #26014982 | C2 | semidirect |
| 8. Q8×Dic353 | C2 | semidirect |
| 9. #26014957 | C2 | semidirect |
| 67. C353 | #541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26014990 | 2 |
| #26014985 | 2 |
| #26014983 | 2 |
| #26014982 | 2 |
| #26014971 | 2 |
| Q8×Dic353 | 2 |
| #26014957 | 2 |
| #26014951 | 2 |
| C22⋊Q8×C353 | 2 |
| #541 | 353 |