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×#19153824 | C2 | semidirect |
| 2. #26041857 | C2 | semidirect |
| 3. #26041846 | C2 | semidirect |
| 4. #26041529 | C2 | semidirect |
| 5. #26041522 | C2 | semidirect |
| 6. #26041512 | C2 | semidirect |
| 7. #26041505 | C2 | semidirect |
| 8. #26041321 | C2 | semidirect |
| 9. #26041275 | C2 | semidirect |
| 10. C2×#19153737 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C181 | C2 | semidirect |
| 14. C2×#15668432 | C22 | semidirect |
| 16. C2×C8×D181 | C22 | semidirect |
| 20. #19153792 | C22 | semidirect |
| 25. #19153787 | C22 | semidirect |
| 29. #19153750 | C22 | semidirect |
| 30. #19153748 | C22 | semidirect |
| 31. #19153740 | C22 | semidirect |
| 32. #19153740 | C22 | semidirect |
| 35. #19153737 | C22 | semidirect |
| 36. #19153737 | C22 | semidirect |
| 83. M16×C181 | D4 | semidirect |
| 151. C181 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D181 | semidirect |
| 220. M16 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153824 | 2 |
| #26041857 | 2 |
| #26041846 | 2 |
| #26041529 | 2 |
| #26041522 | 2 |
| #26041512 | 2 |
| #26041505 | 2 |
| #26041321 | 2 |
| #26041275 | 2 |
| C2×#19153737 | 2 |
| C2×AGL(1,ℤ/8)×C181 | 2 |
| #3062 | 181 |