Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 492 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. #26012036 | C2 | semidirect |
| 2. C2×D4×Dic173 | C2 | semidirect |
| 3. #26011805 | C2 | semidirect |
| 4. #26011802 | C2 | semidirect |
| 5. #26011769 | C2 | semidirect |
| 6. #26011684 | C2 | semidirect |
| 7. #26011625 | C2 | semidirect |
| 8. D8×Dic173 | C2 | semidirect |
| 9. #26011571 | C2 | semidirect |
| 10. #26011541 | C2 | semidirect |
| 11. #447×C173 | C2 | semidirect |
| 15. #19149678 | C22 | semidirect |
| 16. #19149675 | C22 | semidirect |
| 24. D4×Dic173 | C22 | semidirect |
| 25. #19149641 | C22 | semidirect |
| 30. #19149613 | C22 | semidirect |
| 31. #19149612 | C22 | semidirect |
| 32. #19149608 | C22 | semidirect |
| 33. #19149601 | C22 | semidirect |
| 35. #19149600 | C22 | semidirect |
| 37. C8×Dic173 | C22 | semidirect |
| 96. C2×Dic173 | D8 | semidirect |
| 113. D4×C173 | #41 | semidirect |
| 149. C173 | #3100 | semidirect |
| 158. #447 | D173 | semidirect |
| 249. D4 | #14583825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012036 | 2 |
| C2×D4×Dic173 | 2 |
| #26011805 | 2 |
| #26011802 | 2 |
| #26011769 | 2 |
| #26011684 | 2 |
| #26011625 | 2 |
| D8×Dic173 | 2 |
| #26011571 | 2 |
| #26011541 | 2 |
| #447×C173 | 2 |
| #3100 | 173 |