Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #26042077 | C2 | semidirect |
| 2. C2×#19153842 | C2 | semidirect |
| 3. #26042046 | C2 | semidirect |
| 4. #26041547 | C2 | semidirect |
| 5. #26041540 | C2 | semidirect |
| 6. #26041327 | C2 | semidirect |
| 7. #26041261 | C2 | semidirect |
| 8. C2×#19153733 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C181 | C2 | semidirect |
| 12. #19153846 | C22 | semidirect |
| 16. #19153841 | C22 | semidirect |
| 18. C2×#15668437 | C22 | semidirect |
| 19. C2×#15668434 | C22 | semidirect |
| 21. #19153823 | C22 | semidirect |
| 26. #19153751 | C22 | semidirect |
| 27. #19153734 | C22 | semidirect |
| 28. #19153733 | C22 | semidirect |
| 29. #19153732 | C22 | semidirect |
| 147. C181 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042077 | 2 |
| C2×#19153842 | 2 |
| #26042046 | 2 |
| #26041547 | 2 |
| #26041540 | 2 |
| #26041327 | 2 |
| #26041261 | 2 |
| C2×#19153733 | 2 |
| C2×AGL(1,ℤ/8)×C181 | 2 |
| #3068 | 181 |