Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26014986 | C2 | semidirect |
| 2. #26014984 | C2 | semidirect |
| 3. #26014980 | C2 | semidirect |
| 4. #26014975 | C2 | semidirect |
| 5. #26014971 | C2 | semidirect |
| 7. C4×Dic706 | C2 | semidirect |
| 8. C4×D1412 | C2 | semidirect |
| 9. C4×C22⋊D353 | C2 | semidirect |
| 10. #26014949 | C2 | semidirect |
| 11. C2×C42×C353 | C2 | semidirect |
| 74. C353 | #529 | semidirect |
| 86. C2×C42 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26014986 | 2 |
| #26014984 | 2 |
| #26014980 | 2 |
| #26014975 | 2 |
| #26014971 | 2 |
| #26014966 | 2 |
| C4×Dic706 | 2 |
| C4×D1412 | 2 |
| C4×C22⋊D353 | 2 |
| #26014949 | 2 |
| C2×C42×C353 | 2 |
| #529 | 353 |