Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26041834 | C2 | semidirect |
| 3. #26041671 | C2 | semidirect |
| 4. #26041639 | C2 | semidirect |
| 5. #26041638 | C2 | semidirect |
| 6. #26041487 | C2 | semidirect |
| 7. #26041477 | C2 | semidirect |
| 8. #26041440 | C2 | semidirect |
| 9. #26041438 | C2 | semidirect |
| 10. #26041334 | C2 | semidirect |
| 11. #497×C181 | C2 | semidirect |
| 141. C181 | #3216 | semidirect |
| 146. #497 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| #26041828 | 2 |
| #26041671 | 2 |
| #26041639 | 2 |
| #26041638 | 2 |
| #26041487 | 2 |
| #26041477 | 2 |
| #26041440 | 2 |
| #26041438 | 2 |
| #26041334 | 2 |
| #497×C181 | 2 |
| #3216 | 181 |