Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
454 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041815 | C2 | semidirect |
| 2. C2×D4×Dic181 | C2 | semidirect |
| 3. #26041612 | C2 | semidirect |
| 4. #26041598 | C2 | semidirect |
| 5. #26041581 | C2 | semidirect |
| 6. #26041496 | C2 | semidirect |
| 8. SD16×Dic181 | C2 | semidirect |
| 9. #26041359 | C2 | semidirect |
| 10. #26041329 | C2 | semidirect |
| 11. #450×C181 | C2 | semidirect |
| 15. #19153807 | C22 | semidirect |
| 16. #19153805 | C22 | semidirect |
| 19. Q8×Dic181 | C22 | semidirect |
| 24. #19153778 | C22 | semidirect |
| 30. #19153749 | C22 | semidirect |
| 31. #19153748 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 33. #19153740 | C22 | semidirect |
| 34. #19153738 | C22 | semidirect |
| 37. C8×Dic181 | C22 | semidirect |
| 140. C181 | #3105 | semidirect |
| 148. #450 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041815 | 2 |
| C2×D4×Dic181 | 2 |
| #26041612 | 2 |
| #26041598 | 2 |
| #26041581 | 2 |
| #26041496 | 2 |
| #26041413 | 2 |
| SD16×Dic181 | 2 |
| #26041359 | 2 |
| #26041329 | 2 |
| #450×C181 | 2 |
| #3105 | 181 |