Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. C2×#19149710 | C2 | semidirect |
| 3. #26012065 | C2 | semidirect |
| 4. #26011672 | C2 | semidirect |
| 5. #26011667 | C2 | semidirect |
| 6. #26011508 | C2 | semidirect |
| 7. #26011507 | C2 | semidirect |
| 8. #26011473 | C2 | semidirect |
| 9. C2×#137×C173 | C2 | semidirect |
| 23. #19149710 | C22 | semidirect |
| 26. C2×#14583810 | C22 | semidirect |
| 27. #19149677 | C22 | semidirect |
| 28. #19149668 | C22 | semidirect |
| 31. #19149638 | C22 | semidirect |
| 32. #19149606 | C22 | semidirect |
| 33. #19149605 | C22 | semidirect |
| 34. #19149597 | C22 | semidirect |
| 35. #19149595 | C22 | semidirect |
| 37. C22×Q8×C173 | C22 | semidirect |
| 39. #137×C173 | C22 | semidirect |
| 42. C2×M16×C173 | C22 | semidirect |
| 192. C173 | #3022 | semidirect |
| 196. C2×#137 | D173 | semidirect |
| 216. C22×Q8 | C2×D173 | semidirect |
| 220. #137 | C2×D173 | semidirect |
| 226. C2×M16 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012327 | 2 |
| C2×#19149710 | 2 |
| #26012065 | 2 |
| #26011672 | 2 |
| #26011667 | 2 |
| #26011508 | 2 |
| #26011507 | 2 |
| #26011473 | 2 |
| C2×#137×C173 | 2 |
| #3022 | 173 |