Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
444 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 444 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. #26041831 | C2 | semidirect |
| 3. #26041615 | C2 | semidirect |
| 4. #26041612 | C2 | semidirect |
| 5. #26041557 | C2 | semidirect |
| 6. #26041482 | C2 | semidirect |
| 8. #26041380 | C2 | semidirect |
| 9. #26041376 | C2 | semidirect |
| 10. #26041333 | C2 | semidirect |
| 14. #19153815 | C22 | semidirect |
| 15. #19153814 | C22 | semidirect |
| 19. Q8×Dic181 | C22 | semidirect |
| 21. #19153781 | C22 | semidirect |
| 30. #19153750 | C22 | semidirect |
| 31. #19153749 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 33. #19153741 | C22 | semidirect |
| 34. #19153740 | C22 | semidirect |
| 37. #19153726 | C22 | semidirect |
| 136. C181 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041831 | 2 |
| C2×D4×Dic181 | 2 |
| #26041615 | 2 |
| #26041612 | 2 |
| #26041557 | 2 |
| #26041482 | 2 |
| #26041430 | 2 |
| #26041380 | 2 |
| #26041376 | 2 |
| #26041333 | 2 |
| #450×C181 | 2 |
| #3110 | 181 |