Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 2. C22×#15668437 | C2 | semidirect |
| 3. #26041855 | C2 | semidirect |
| 4. #26041494 | C2 | semidirect |
| 5. #26041484 | C2 | semidirect |
| 6. #26041306 | C2 | semidirect |
| 7. #26041287 | C2 | semidirect |
| 8. #26041273 | C2 | semidirect |
| 9. #518×C181 | C2 | semidirect |
| 19. #19153816 | C22 | semidirect |
| 20. #19153804 | C22 | semidirect |
| 23. C4⋊#13089678 | C22 | semidirect |
| 24. #19153739 | C22 | semidirect |
| 25. #19153739 | C22 | semidirect |
| 26. #19153736 | C22 | semidirect |
| 116. C181 | #3042 | semidirect |
| 121. #518 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153842 | 2 |
| C22×#15668437 | 2 |
| #26041855 | 2 |
| #26041494 | 2 |
| #26041484 | 2 |
| #26041306 | 2 |
| #26041287 | 2 |
| #26041273 | 2 |
| #518×C181 | 2 |
| #3042 | 181 |