Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#15668434 | C2 | semidirect |
| 2. C2×#19153824 | C2 | semidirect |
| 3. #26041848 | C2 | semidirect |
| 4. #26041846 | C2 | semidirect |
| 5. #26041531 | C2 | semidirect |
| 6. #26041514 | C2 | semidirect |
| 7. #26041315 | C2 | semidirect |
| 8. #26041285 | C2 | semidirect |
| 9. #418×C181 | C2 | semidirect |
| 16. C2×#15668432 | C22 | semidirect |
| 18. C2×C8×D181 | C22 | semidirect |
| 23. #19153791 | C22 | semidirect |
| 24. #19153787 | C22 | semidirect |
| 28. #19153749 | C22 | semidirect |
| 29. #19153747 | C22 | semidirect |
| 30. #19153738 | C22 | semidirect |
| 34. #102×C181 | C22 | semidirect |
| 51. C2×#13089678 | D4 | semidirect |
| 125. C181 | #3058 | semidirect |
| 135. #418 | D181 | semidirect |
| 160. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668434 | 2 |
| C2×#19153824 | 2 |
| #26041848 | 2 |
| #26041846 | 2 |
| #26041531 | 2 |
| #26041514 | 2 |
| #26041315 | 2 |
| #26041285 | 2 |
| #418×C181 | 2 |
| #3058 | 181 |