Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
366 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 366 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. #26041686 | C2 | semidirect |
| 4. #26041642 | C2 | semidirect |
| 5. #26041605 | C2 | semidirect |
| 6. #26041601 | C2 | semidirect |
| 7. #26041566 | C2 | semidirect |
| 8. #26041560 | C2 | semidirect |
| 9. #26041559 | C2 | semidirect |
| 10. #26041335 | C2 | semidirect |
| 11. #476×C181 | C2 | semidirect |
| 138. C181 | #3235 | semidirect |
| 147. #476 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| #26041826 | 2 |
| #26041686 | 2 |
| #26041642 | 2 |
| #26041605 | 2 |
| #26041601 | 2 |
| #26041566 | 2 |
| #26041560 | 2 |
| #26041559 | 2 |
| #26041335 | 2 |
| #476×C181 | 2 |
| #3235 | 181 |