Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041813 | C2 | semidirect |
| 2. #26041666 | C2 | semidirect |
| 3. #26041643 | C2 | semidirect |
| 4. #26041476 | C2 | semidirect |
| 5. #26041471 | C2 | semidirect |
| 6. #26041430 | C2 | semidirect |
| 7. #26041413 | C2 | semidirect |
| 8. #26041336 | C2 | semidirect |
| 9. C2×#127×C181 | C2 | semidirect |
| 10. C2×#15668437 | C22 | semidirect |
| 11. C2×#15668434 | C22 | semidirect |
| 13. #19153808 | C22 | semidirect |
| 14. #19153804 | C22 | semidirect |
| 18. C4×Dic362 | C22 | semidirect |
| 19. C4×D724 | C22 | semidirect |
| 22. C4⋊#13089678 | C22 | semidirect |
| 23. #19153737 | C22 | semidirect |
| 24. #19153737 | C22 | semidirect |
| 26. #19153727 | C22 | semidirect |
| 127. C181 | #3217 | semidirect |
| 129. C2×#127 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041813 | 2 |
| #26041666 | 2 |
| #26041643 | 2 |
| #26041476 | 2 |
| #26041471 | 2 |
| #26041430 | 2 |
| #26041413 | 2 |
| #26041336 | 2 |
| C2×#127×C181 | 2 |
| #3217 | 181 |