Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26041933 | C2 | semidirect |
| 2. #26041625 | C2 | semidirect |
| 3. #26041590 | C2 | semidirect |
| 4. #26041559 | C2 | semidirect |
| 5. #26041513 | C2 | semidirect |
| 6. #26041471 | C2 | semidirect |
| 7. #26041413 | C2 | semidirect |
| 8. C4×#15668434 | C2 | semidirect |
| 9. D4×#13089678 | C2 | semidirect |
| 10. C2×#19153737 | C2 | semidirect |
| 11. D42×C181 | C2 | semidirect |
| 14. C2×#15668434 | C22 | semidirect |
| 15. C22×#13089678 | C22 | semidirect |
| 16. #19153816 | C22 | semidirect |
| 19. #19153790 | C22 | semidirect |
| 20. C4×D724 | C22 | semidirect |
| 21. C2×C4⋊Dic181 | C22 | semidirect |
| 22. #19153749 | C22 | semidirect |
| 23. #19153749 | C22 | semidirect |
| 24. C4⋊#13089678 | C22 | semidirect |
| 27. #19153737 | C22 | semidirect |
| 28. #19153737 | C22 | semidirect |
| 29. #19153737 | C22 | semidirect |
| 30. #19153736 | C22 | semidirect |
| 31. C22⋊#13089678 | C22 | semidirect |
| 32. C4×#13089678 | C22 | semidirect |
| 103. D4×C181 | D8 | semidirect |
| 104. D4×C181 | #41 | semidirect |
| 142. C181 | #3294 | semidirect |
| 145. D42 | D181 | semidirect |
| 239. D4 | #15668434 | semidirect |
| 240. D4 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041933 | 2 |
| #26041625 | 2 |
| #26041590 | 2 |
| #26041559 | 2 |
| #26041513 | 2 |
| #26041471 | 2 |
| #26041413 | 2 |
| C4×#15668434 | 2 |
| D4×#13089678 | 2 |
| C2×#19153737 | 2 |
| D42×C181 | 2 |
| #3294 | 181 |