Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041884 | C2 | semidirect |
| 2. #26041855 | C2 | semidirect |
| 3. #26041668 | C2 | semidirect |
| 4. #26041652 | C2 | semidirect |
| 5. #26041648 | C2 | semidirect |
| 6. #26041634 | C2 | semidirect |
| 7. #26041495 | C2 | semidirect |
| 8. #26041485 | C2 | semidirect |
| 9. #26041426 | C2 | semidirect |
| 10. #26041420 | C2 | semidirect |
| 11. #433×C181 | C2 | semidirect |
| 120. C181 | #3221 | semidirect |
| 132. #433 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041884 | 2 |
| #26041855 | 2 |
| #26041668 | 2 |
| #26041652 | 2 |
| #26041648 | 2 |
| #26041634 | 2 |
| #26041495 | 2 |
| #26041485 | 2 |
| #26041426 | 2 |
| #26041420 | 2 |
| #433×C181 | 2 |
| #3221 | 181 |