Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26041829 | C2 | semidirect |
| 2. #26041813 | C2 | semidirect |
| 3. #26041663 | C2 | semidirect |
| 4. #26041634 | C2 | semidirect |
| 5. #26041490 | C2 | semidirect |
| 6. #26041485 | C2 | semidirect |
| 7. #26041480 | C2 | semidirect |
| 8. #26041475 | C2 | semidirect |
| 9. #26041443 | C2 | semidirect |
| 10. #26041426 | C2 | semidirect |
| 11. #431×C181 | C2 | semidirect |
| 144. C181 | #3212 | semidirect |
| 156. #431 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| #26041813 | 2 |
| #26041663 | 2 |
| #26041634 | 2 |
| #26041490 | 2 |
| #26041485 | 2 |
| #26041480 | 2 |
| #26041475 | 2 |
| #26041443 | 2 |
| #26041426 | 2 |
| #431×C181 | 2 |
| #3212 | 181 |