Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012103 | C2 | semidirect |
| 3. #26011885 | C2 | semidirect |
| 4. #26011864 | C2 | semidirect |
| 5. #26011856 | C2 | semidirect |
| 6. #26011846 | C2 | semidirect |
| 7. #26011714 | C2 | semidirect |
| 8. #26011692 | C2 | semidirect |
| 9. #26011655 | C2 | semidirect |
| 10. #26011644 | C2 | semidirect |
| 11. #433×C173 | C2 | semidirect |
| 14. C2×Dic692 | C22 | semidirect |
| 17. C2×#14583815 | C22 | semidirect |
| 18. #19149679 | C22 | semidirect |
| 22. #19149671 | C22 | semidirect |
| 29. C4×Dic346 | C22 | semidirect |
| 30. #19149604 | C22 | semidirect |
| 33. #19149601 | C22 | semidirect |
| 35. C4⋊C8×C173 | C22 | semidirect |
| 37. #97×C173 | C22 | semidirect |
| 38. C4×C8×C173 | C22 | semidirect |
| 122. C173 | #3222 | semidirect |
| 134. #433 | D173 | semidirect |
| 154. C4⋊C8 | C2×D173 | semidirect |
| 160. #97 | C2×D173 | semidirect |
| 161. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012103 | 2 |
| #26012060 | 2 |
| #26011885 | 2 |
| #26011864 | 2 |
| #26011856 | 2 |
| #26011846 | 2 |
| #26011714 | 2 |
| #26011692 | 2 |
| #26011655 | 2 |
| #26011644 | 2 |
| #433×C173 | 2 |
| #3222 | 173 |