Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19149705 | C2 | semidirect |
| 2. C2×#19149701 | C2 | semidirect |
| 3. #26012058 | C2 | semidirect |
| 4. #26011972 | C2 | semidirect |
| 5. #26011712 | C2 | semidirect |
| 6. #26011705 | C2 | semidirect |
| 7. #26011690 | C2 | semidirect |
| 8. #26011685 | C2 | semidirect |
| 9. #26011517 | C2 | semidirect |
| 10. #26011490 | C2 | semidirect |
| 11. C2×#102×C173 | C2 | semidirect |
| 16. C2×Dic692 | C22 | semidirect |
| 17. C2×#14583815 | C22 | semidirect |
| 18. C2×#14583815 | C22 | semidirect |
| 20. C2×D1384 | C22 | semidirect |
| 28. #19149644 | C22 | semidirect |
| 29. #19149641 | C22 | semidirect |
| 34. #19149608 | C22 | semidirect |
| 35. #19149608 | C22 | semidirect |
| 36. #19149602 | C22 | semidirect |
| 37. #19149599 | C22 | semidirect |
| 46. #14583826 | D4 | semidirect |
| 154. C173 | #3045 | semidirect |
| 166. C2×#102 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149705 | 2 |
| C2×#19149701 | 2 |
| #26012058 | 2 |
| #26011972 | 2 |
| #26011712 | 2 |
| #26011705 | 2 |
| #26011690 | 2 |
| #26011685 | 2 |
| #26011517 | 2 |
| #26011490 | 2 |
| C2×#102×C173 | 2 |
| #3045 | 173 |