Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26012104 | C2 | semidirect |
| 3. #26011885 | C2 | semidirect |
| 4. #26011863 | C2 | semidirect |
| 5. #26011848 | C2 | semidirect |
| 6. #26011712 | C2 | semidirect |
| 7. #26011690 | C2 | semidirect |
| 8. #26011654 | C2 | semidirect |
| 9. #26011643 | C2 | semidirect |
| 10. #26011553 | C2 | semidirect |
| 11. #490×C173 | C2 | semidirect |
| 14. C2×Dic692 | C22 | semidirect |
| 17. C2×#14583814 | C22 | semidirect |
| 18. #19149679 | C22 | semidirect |
| 27. #19149644 | C22 | semidirect |
| 29. #19149608 | C22 | semidirect |
| 30. #19149602 | C22 | semidirect |
| 33. C4×#13063436 | C22 | semidirect |
| 35. #125×C173 | C22 | semidirect |
| 37. #102×C173 | C22 | semidirect |
| 38. #97×C173 | C22 | semidirect |
| 122. C173 | #3222 | semidirect |
| 128. #490 | D173 | semidirect |
| 146. #125 | C2×D173 | semidirect |
| 158. #102 | C2×D173 | semidirect |
| 160. #97 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012104 | 2 |
| #26012054 | 2 |
| #26011885 | 2 |
| #26011863 | 2 |
| #26011848 | 2 |
| #26011712 | 2 |
| #26011690 | 2 |
| #26011654 | 2 |
| #26011643 | 2 |
| #26011553 | 2 |
| #490×C173 | 2 |
| #3222 | 173 |