Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26042003 | C2 | semidirect |
| 3. #26041602 | C2 | semidirect |
| 4. #26041556 | C2 | semidirect |
| 5. #26041524 | C2 | semidirect |
| 6. #26041476 | C2 | semidirect |
| 7. #26041431 | C2 | semidirect |
| 8. C4×#15668438 | C2 | semidirect |
| 9. #26041358 | C2 | semidirect |
| 10. #26041282 | C2 | semidirect |
| 11. #486×C181 | C2 | semidirect |
| 15. C2×#15668437 | C22 | semidirect |
| 16. C2×#15668432 | C22 | semidirect |
| 19. #19153796 | C22 | semidirect |
| 24. C4×Dic362 | C22 | semidirect |
| 27. #19153774 | C22 | semidirect |
| 28. #19153749 | C22 | semidirect |
| 29. #19153748 | C22 | semidirect |
| 30. C4⋊#13089678 | C22 | semidirect |
| 31. #19153741 | C22 | semidirect |
| 33. #19153737 | C22 | semidirect |
| 35. #19153728 | C22 | semidirect |
| 36. C4⋊Q8×C181 | C22 | semidirect |
| 38. #102×C181 | C22 | semidirect |
| 39. #102×C181 | C22 | semidirect |
| 40. C4×C8×C181 | C22 | semidirect |
| 135. C181 | #3324 | semidirect |
| 139. #486 | D181 | semidirect |
| 153. C4⋊Q8 | C2×D181 | semidirect |
| 173. #102 | C2×D181 | semidirect |
| 174. #102 | C2×D181 | semidirect |
| 176. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042003 | 2 |
| #26041914 | 2 |
| #26041602 | 2 |
| #26041556 | 2 |
| #26041524 | 2 |
| #26041476 | 2 |
| #26041431 | 2 |
| C4×#15668438 | 2 |
| #26041358 | 2 |
| #26041282 | 2 |
| #486×C181 | 2 |
| #3324 | 181 |