Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19153844 | C2 | semidirect |
| 2. #26041925 | C2 | semidirect |
| 3. #26041663 | C2 | semidirect |
| 4. #26041525 | C2 | semidirect |
| 5. #26041495 | C2 | semidirect |
| 6. #26041443 | C2 | semidirect |
| 7. #26041415 | C2 | semidirect |
| 8. C4×D1448 | C2 | semidirect |
| 9. #436×C181 | C2 | semidirect |
| 11. C22×D724 | C22 | semidirect |
| 13. C2×Dic724 | C22 | semidirect |
| 14. C2×#15668438 | C22 | semidirect |
| 15. C2×#15668438 | C22 | semidirect |
| 19. #19153804 | C22 | semidirect |
| 21. #19153795 | C22 | semidirect |
| 25. C4×D724 | C22 | semidirect |
| 27. #19153750 | C22 | semidirect |
| 28. #19153741 | C22 | semidirect |
| 29. #19153738 | C22 | semidirect |
| 30. #19153738 | C22 | semidirect |
| 31. C2×M16×C181 | C22 | semidirect |
| 33. C4⋊C8×C181 | C22 | semidirect |
| 34. C22⋊C8×C181 | C22 | semidirect |
| 35. C4×C8×C181 | C22 | semidirect |
| 54. D1448 | D4 | semidirect |
| 124. C181 | #3273 | semidirect |
| 134. #436 | D181 | semidirect |
| 144. C2×M16 | C2×D181 | semidirect |
| 155. C4⋊C8 | C2×D181 | semidirect |
| 159. C22⋊C8 | C2×D181 | semidirect |
| 160. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153844 | 2 |
| #26041925 | 2 |
| #26041663 | 2 |
| #26041525 | 2 |
| #26041495 | 2 |
| #26041443 | 2 |
| #26041415 | 2 |
| C4×D1448 | 2 |
| #436×C181 | 2 |
| #3273 | 181 |