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×#19153842 | C2 | semidirect |
| 2. C2×#19153836 | C2 | semidirect |
| 3. #26041759 | C2 | semidirect |
| 4. #26041498 | C2 | semidirect |
| 5. #26041491 | C2 | semidirect |
| 6. #26041476 | C2 | semidirect |
| 7. #26041471 | C2 | semidirect |
| 8. #26041306 | C2 | semidirect |
| 9. #26041280 | C2 | semidirect |
| 10. C2×#19153737 | C2 | semidirect |
| 11. #535×C181 | C2 | semidirect |
| 15. C2×#15668439 | C22 | semidirect |
| 17. C2×#15668437 | C22 | semidirect |
| 18. C2×#15668436 | C22 | semidirect |
| 20. C2×#15668434 | C22 | semidirect |
| 23. C4×Dic362 | C22 | semidirect |
| 24. C4×D724 | C22 | semidirect |
| 29. C4⋊#13089678 | C22 | semidirect |
| 30. C4⋊#13089678 | C22 | semidirect |
| 31. #19153740 | C22 | semidirect |
| 34. #19153737 | C22 | semidirect |
| 44. #15668449 | D4 | semidirect |
| 154. C181 | #3045 | semidirect |
| 158. #535 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153842 | 2 |
| C2×#19153836 | 2 |
| #26041759 | 2 |
| #26041498 | 2 |
| #26041491 | 2 |
| #26041476 | 2 |
| #26041471 | 2 |
| #26041306 | 2 |
| #26041280 | 2 |
| C2×#19153737 | 2 |
| #535×C181 | 2 |
| #3045 | 181 |