Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26041885 | C2 | semidirect |
| 2. #26041854 | C2 | semidirect |
| 3. #26041668 | C2 | semidirect |
| 4. #26041653 | C2 | semidirect |
| 5. #26041636 | C2 | semidirect |
| 6. #26041497 | C2 | semidirect |
| 7. #26041483 | C2 | semidirect |
| 8. #26041427 | C2 | semidirect |
| 9. #26041419 | C2 | semidirect |
| 10. #26041341 | C2 | semidirect |
| 11. #491×C181 | C2 | semidirect |
| 120. C181 | #3221 | semidirect |
| 126. #491 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041885 | 2 |
| #26041854 | 2 |
| #26041668 | 2 |
| #26041653 | 2 |
| #26041636 | 2 |
| #26041497 | 2 |
| #26041483 | 2 |
| #26041427 | 2 |
| #26041419 | 2 |
| #26041341 | 2 |
| #491×C181 | 2 |
| #3221 | 181 |