Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
414 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C2×#19149658 | C2 | semidirect |
| 3. #26011833 | C2 | semidirect |
| 4. #26011827 | C2 | semidirect |
| 5. #26011810 | C2 | semidirect |
| 6. #26011749 | C2 | semidirect |
| 7. #26011737 | C2 | semidirect |
| 8. #26011655 | C2 | semidirect |
| 9. #26011649 | C2 | semidirect |
| 10. #26011632 | C2 | semidirect |
| 11. #407×C173 | C2 | semidirect |
| 14. C2×Dic692 | C22 | semidirect |
| 15. C2×#14583815 | C22 | semidirect |
| 32. #19149613 | C22 | semidirect |
| 33. #19149611 | C22 | semidirect |
| 34. #19149604 | C22 | semidirect |
| 35. #19149604 | C22 | semidirect |
| 36. #19149604 | C22 | semidirect |
| 37. #19149601 | C22 | semidirect |
| 149. C173 | #3196 | semidirect |
| 161. #407 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012002 | 2 |
| C2×#19149658 | 2 |
| #26011833 | 2 |
| #26011827 | 2 |
| #26011810 | 2 |
| #26011749 | 2 |
| #26011737 | 2 |
| #26011655 | 2 |
| #26011649 | 2 |
| #26011632 | 2 |
| #407×C173 | 2 |
| #3196 | 173 |