Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#19153804 | C2 | semidirect |
| 3. #26041663 | C2 | semidirect |
| 4. #26041634 | C2 | semidirect |
| 5. #26041502 | C2 | semidirect |
| 6. #26041495 | C2 | semidirect |
| 7. #26041437 | C2 | semidirect |
| 8. #26041432 | C2 | semidirect |
| 9. #26041420 | C2 | semidirect |
| 11. #431×C181 | C2 | semidirect |
| 14. C2×Dic724 | C22 | semidirect |
| 16. C2×#15668438 | C22 | semidirect |
| 19. #19153808 | C22 | semidirect |
| 24. #19153804 | C22 | semidirect |
| 28. C4×Dic362 | C22 | semidirect |
| 29. C4×D724 | C22 | semidirect |
| 34. #19153741 | C22 | semidirect |
| 35. #19153741 | C22 | semidirect |
| 39. C4⋊C8×C181 | C22 | semidirect |
| 42. C4×C8×C181 | C22 | semidirect |
| 143. C181 | #3211 | semidirect |
| 155. #431 | D181 | semidirect |
| 179. C4⋊C8 | C2×D181 | semidirect |
| 186. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041813 | 2 |
| C2×#19153804 | 2 |
| #26041663 | 2 |
| #26041634 | 2 |
| #26041502 | 2 |
| #26041495 | 2 |
| #26041437 | 2 |
| #26041432 | 2 |
| #26041420 | 2 |
| #26041415 | 2 |
| #431×C181 | 2 |
| #3211 | 181 |