Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19153847 | C2 | semidirect |
| 3. C2×#19153805 | C2 | semidirect |
| 4. #26041747 | C2 | semidirect |
| 5. #26041504 | C2 | semidirect |
| 6. #26041497 | C2 | semidirect |
| 7. #26041302 | C2 | semidirect |
| 8. #26041283 | C2 | semidirect |
| 9. #419×C181 | C2 | semidirect |
| 14. C2×#15668439 | C22 | semidirect |
| 16. C2×#15668436 | C22 | semidirect |
| 22. #19153781 | C22 | semidirect |
| 23. #19153778 | C22 | semidirect |
| 29. #19153745 | C22 | semidirect |
| 34. #103×C181 | C22 | semidirect |
| 125. C181 | #3040 | semidirect |
| 134. #419 | D181 | semidirect |
| 159. #103 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153847 | 2 |
| C2×#19153844 | 2 |
| C2×#19153805 | 2 |
| #26041747 | 2 |
| #26041504 | 2 |
| #26041497 | 2 |
| #26041302 | 2 |
| #26041283 | 2 |
| #419×C181 | 2 |
| #3040 | 181 |