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×#19153836 | C2 | semidirect |
| 2. #26041846 | C2 | semidirect |
| 3. #26041762 | C2 | semidirect |
| 4. #26041499 | C2 | semidirect |
| 5. #26041492 | C2 | semidirect |
| 6. #26041477 | C2 | semidirect |
| 7. #26041472 | C2 | semidirect |
| 8. #26041307 | C2 | semidirect |
| 9. #26041281 | C2 | semidirect |
| 10. C2×#19153737 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C181 | C2 | semidirect |
| 14. C2×#15668439 | C22 | semidirect |
| 15. C2×#15668437 | C22 | semidirect |
| 16. C2×#15668436 | C22 | semidirect |
| 17. C2×#15668434 | C22 | semidirect |
| 24. Q8×Dic181 | C22 | semidirect |
| 26. D4×Dic181 | C22 | semidirect |
| 31. #19153745 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 33. #19153741 | C22 | semidirect |
| 34. #19153738 | C22 | semidirect |
| 73. #41×C181 | D4 | semidirect |
| 154. C181 | #3045 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D181 | semidirect |
| 202. #41 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153836 | 2 |
| #26041846 | 2 |
| #26041762 | 2 |
| #26041499 | 2 |
| #26041492 | 2 |
| #26041477 | 2 |
| #26041472 | 2 |
| #26041307 | 2 |
| #26041281 | 2 |
| C2×#19153737 | 2 |
| C2×AGL(1,ℤ/8)×C181 | 2 |
| #3045 | 181 |