Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012202 | C2 | semidirect |
| 3. #26011839 | C2 | semidirect |
| 4. #26011811 | C2 | semidirect |
| 5. #26011721 | C2 | semidirect |
| 6. #26011692 | C2 | semidirect |
| 7. #26011643 | C2 | semidirect |
| 8. C4×#14583814 | C2 | semidirect |
| 9. #26011556 | C2 | semidirect |
| 10. #102×D173 | C2 | semidirect |
| 11. #476×C173 | C2 | semidirect |
| 14. C2×#14583815 | C22 | semidirect |
| 16. C2×C8×D173 | C22 | semidirect |
| 19. #19149659 | C22 | semidirect |
| 24. C4×Dic346 | C22 | semidirect |
| 27. C4⋊C4×D173 | C22 | semidirect |
| 28. #19149610 | C22 | semidirect |
| 29. #19149602 | C22 | semidirect |
| 30. #19149601 | C22 | semidirect |
| 32. #19149599 | C22 | semidirect |
| 33. #19149599 | C22 | semidirect |
| 34. #19149591 | C22 | semidirect |
| 35. C4×#13063436 | C22 | semidirect |
| 36. C4⋊Q8×C173 | C22 | semidirect |
| 38. #106×C173 | C22 | semidirect |
| 39. C4⋊C8×C173 | C22 | semidirect |
| 89. D692 | SD16 | semidirect |
| 136. C173 | #3295 | semidirect |
| 142. #476 | D173 | semidirect |
| 154. C4⋊Q8 | C2×D173 | semidirect |
| 168. #106 | C2×D173 | semidirect |
| 169. C4⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012202 | 2 |
| D4×D692 | 2 |
| #26011839 | 2 |
| #26011811 | 2 |
| #26011721 | 2 |
| #26011692 | 2 |
| #26011643 | 2 |
| C4×#14583814 | 2 |
| #26011556 | 2 |
| #102×D173 | 2 |
| #476×C173 | 2 |
| #3295 | 173 |