Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 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 |
|---|---|---|
| 1. C2×#19153842 | C2 | semidirect |
| 2. C22×#15668434 | C2 | semidirect |
| 3. #26041848 | C2 | semidirect |
| 4. #26041494 | C2 | semidirect |
| 5. #26041474 | C2 | semidirect |
| 6. #26041306 | C2 | semidirect |
| 7. #26041283 | C2 | semidirect |
| 8. #26041273 | C2 | semidirect |
| 9. #518×C181 | C2 | semidirect |
| 13. C2×#15668437 | C22 | semidirect |
| 16. C2×#15668434 | C22 | semidirect |
| 19. #19153813 | C22 | semidirect |
| 20. #19153804 | C22 | semidirect |
| 23. C4⋊#13089678 | C22 | semidirect |
| 24. #19153739 | C22 | semidirect |
| 25. #19153736 | C22 | semidirect |
| 26. #19153736 | C22 | semidirect |
| 29. C4×D4×C181 | C22 | semidirect |
| 56. C2×D4×C181 | D4 | semidirect |
| 121. C181 | #3041 | semidirect |
| 126. #518 | D181 | semidirect |
| 147. C4×D4 | C2×D181 | semidirect |
| 169. C2×D4 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153842 | 2 |
| C22×#15668434 | 2 |
| #26041848 | 2 |
| #26041494 | 2 |
| #26041474 | 2 |
| #26041306 | 2 |
| #26041283 | 2 |
| #26041273 | 2 |
| #518×C181 | 2 |
| #3041 | 181 |