Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #26042245 | C2 | semidirect |
| 4. #26042238 | C2 | semidirect |
| 5. #26042154 | C2 | semidirect |
| 6. #26042150 | C2 | semidirect |
| 8. #19153904 | C4 | semidirect |
| 10. #19153903 | C4 | semidirect |
| 17. #19153879 | C4 | semidirect |
| 18. #19153878 | C4 | semidirect |
| 25. #19153744 | C4 | semidirect |
| 26. #19153743 | C4 | semidirect |
| 27. #19153742 | C4 | semidirect |
| 28. #104×C181 | C4 | semidirect |
| 120. C181 | #1765 | semidirect |
| 144. #104 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊#131 | 2 |
| #26042269 | 2 |
| #26042245 | 2 |
| #26042238 | 2 |
| #26042154 | 2 |
| #26042150 | 2 |
| #104×D181 | 2 |
| #1765 | 181 |