Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#19153823 | C2 | semidirect |
| 3. #26041843 | C2 | semidirect |
| 4. #26041530 | C2 | semidirect |
| 5. #26041527 | C2 | semidirect |
| 6. #26041513 | C2 | semidirect |
| 7. #26041510 | C2 | semidirect |
| 8. #26041319 | C2 | semidirect |
| 9. #26041275 | C2 | semidirect |
| 10. C2×#19153736 | C2 | semidirect |
| 11. #537×C181 | C2 | semidirect |
| 18. C2×#15668433 | C22 | semidirect |
| 20. C22×#13089678 | C22 | semidirect |
| 27. #19153749 | C22 | semidirect |
| 28. #19153747 | C22 | semidirect |
| 29. #19153740 | C22 | semidirect |
| 30. #19153740 | C22 | semidirect |
| 31. #19153737 | C22 | semidirect |
| 32. #19153737 | C22 | semidirect |
| 38. C22⋊Q8×C181 | C22 | semidirect |
| 41. #121×C181 | C22 | semidirect |
| 53. #15668433 | D4 | semidirect |
| 151. C181 | #3062 | semidirect |
| 155. #537 | D181 | semidirect |
| 178. C22⋊Q8 | C2×D181 | semidirect |
| 183. #121 | 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 |
| C2×#19153823 | 2 |
| #26041843 | 2 |
| #26041530 | 2 |
| #26041527 | 2 |
| #26041513 | 2 |
| #26041510 | 2 |
| #26041319 | 2 |
| #26041275 | 2 |
| C2×#19153736 | 2 |
| #537×C181 | 2 |
| #3062 | 181 |