Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
434 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 434 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. #26041830 | C2 | semidirect |
| 2. #26041828 | C2 | semidirect |
| 3. #26041669 | C2 | semidirect |
| 4. #26041668 | C2 | semidirect |
| 5. #26041641 | C2 | semidirect |
| 6. #26041483 | C2 | semidirect |
| 7. #26041473 | C2 | semidirect |
| 8. #26041427 | C2 | semidirect |
| 9. #26041425 | C2 | semidirect |
| 10. #26041334 | C2 | semidirect |
| 11. #489×C181 | C2 | semidirect |
| 149. C181 | #3214 | semidirect |
| 156. #489 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041830 | 2 |
| #26041828 | 2 |
| #26041669 | 2 |
| #26041668 | 2 |
| #26041641 | 2 |
| #26041483 | 2 |
| #26041473 | 2 |
| #26041427 | 2 |
| #26041425 | 2 |
| #26041334 | 2 |
| #489×C181 | 2 |
| #3214 | 181 |