Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
348 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26041589 | C2 | semidirect |
| 4. #26041571 | C2 | semidirect |
| 5. #26041538 | C2 | semidirect |
| 7. #26041500 | C2 | semidirect |
| 8. #26041490 | C2 | semidirect |
| 9. #26041484 | C2 | semidirect |
| 10. #26041301 | C2 | semidirect |
| 11. #476×C181 | C2 | semidirect |
| 133. C181 | #3252 | semidirect |
| 139. #476 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| #26041811 | 2 |
| #26041589 | 2 |
| #26041571 | 2 |
| #26041538 | 2 |
| #26041524 | 2 |
| #26041500 | 2 |
| #26041490 | 2 |
| #26041484 | 2 |
| #26041301 | 2 |
| #476×C181 | 2 |
| #3252 | 181 |