Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19153841 | C2 | semidirect |
| 2. C22×#15668434 | C2 | semidirect |
| 3. #26041753 | C2 | semidirect |
| 4. #26041491 | C2 | semidirect |
| 5. #26041471 | C2 | semidirect |
| 6. #26041306 | C2 | semidirect |
| 7. #26041284 | C2 | semidirect |
| 8. #26041275 | C2 | semidirect |
| 9. #535×C181 | C2 | semidirect |
| 12. C2×#15668436 | C22 | semidirect |
| 15. C2×#15668434 | C22 | semidirect |
| 18. C4×D724 | C22 | semidirect |
| 22. C4⋊#13089678 | C22 | semidirect |
| 23. #19153740 | C22 | semidirect |
| 24. #19153737 | C22 | semidirect |
| 25. #19153737 | C22 | semidirect |
| 28. #127×C181 | C22 | semidirect |
| 29. #124×C181 | C22 | semidirect |
| 36. C2×D724 | D4 | semidirect |
| 121. C181 | #3041 | semidirect |
| 125. #535 | D181 | semidirect |
| 142. #127 | C2×D181 | semidirect |
| 143. #124 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153841 | 2 |
| C22×#15668434 | 2 |
| #26041753 | 2 |
| #26041491 | 2 |
| #26041471 | 2 |
| #26041306 | 2 |
| #26041284 | 2 |
| #26041275 | 2 |
| #535×C181 | 2 |
| #3041 | 181 |