Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 532 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. #26012039 | C2 | semidirect |
| 2. #127×D173 | C2 | semidirect |
| 3. #26011867 | C2 | semidirect |
| 4. #26011838 | C2 | semidirect |
| 5. #26011837 | C2 | semidirect |
| 6. #26011684 | C2 | semidirect |
| 7. #26011623 | C2 | semidirect |
| 8. #26011542 | C2 | semidirect |
| 9. #493×C173 | C2 | semidirect |
| 14. C2×#14583811 | C22 | semidirect |
| 15. #19149679 | C22 | semidirect |
| 24. D4×Dic173 | C22 | semidirect |
| 26. #19149608 | C22 | semidirect |
| 27. #19149601 | C22 | semidirect |
| 28. #19149600 | C22 | semidirect |
| 30. C4×#13063436 | C22 | semidirect |
| 31. C2×D8×C173 | C22 | semidirect |
| 33. #127×C173 | C22 | semidirect |
| 34. C4×C8×C173 | C22 | semidirect |
| 90. C4×D173 | D8 | semidirect |
| 132. C173 | #3205 | semidirect |
| 137. #493 | D173 | semidirect |
| 148. C2×D8 | C2×D173 | semidirect |
| 155. #127 | C2×D173 | semidirect |
| 167. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012039 | 2 |
| #127×D173 | 2 |
| #26011867 | 2 |
| #26011838 | 2 |
| #26011837 | 2 |
| #26011684 | 2 |
| #26011623 | 2 |
| #26011542 | 2 |
| #493×C173 | 2 |
| #3205 | 173 |