Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26012044 | C2 | semidirect |
| 3. #26011854 | C2 | semidirect |
| 4. #26011836 | C2 | semidirect |
| 5. #26011497 | C2 | semidirect |
| 6. #26011496 | C2 | semidirect |
| 7. #26011495 | C2 | semidirect |
| 8. M16×Dic173 | C2 | semidirect |
| 9. #418×C173 | C2 | semidirect |
| 13. #19149678 | C22 | semidirect |
| 17. #19149670 | C22 | semidirect |
| 22. #19149601 | C22 | semidirect |
| 23. #19149600 | C22 | semidirect |
| 24. #19149599 | C22 | semidirect |
| 25. #19149589 | C22 | semidirect |
| 26. C8×Dic173 | C22 | semidirect |
| 30. #102×C173 | C22 | semidirect |
| 111. C173 | #3138 | semidirect |
| 120. #418 | D173 | semidirect |
| 140. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012044 | 2 |
| C2×#19149675 | 2 |
| #26011854 | 2 |
| #26011836 | 2 |
| #26011497 | 2 |
| #26011496 | 2 |
| #26011495 | 2 |
| M16×Dic173 | 2 |
| #418×C173 | 2 |
| #3138 | 173 |