Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26012119 | C2 | semidirect |
| 3. #26011856 | C2 | semidirect |
| 4. #26011851 | C2 | semidirect |
| 5. #26011846 | C2 | semidirect |
| 6. #26011838 | C2 | semidirect |
| 7. #26011497 | C2 | semidirect |
| 8. #26011493 | C2 | semidirect |
| 9. #26011488 | C2 | semidirect |
| 10. C2×#19149601 | C2 | semidirect |
| 11. #405×C173 | C2 | semidirect |
| 14. #19149679 | C22 | semidirect |
| 17. #19149671 | C22 | semidirect |
| 26. #19149604 | C22 | semidirect |
| 27. #19149604 | C22 | semidirect |
| 28. #19149604 | C22 | semidirect |
| 33. #19149601 | C22 | semidirect |
| 34. #19149601 | C22 | semidirect |
| 35. #19149601 | C22 | semidirect |
| 39. #97×C173 | C22 | semidirect |
| 40. C4×C8×C173 | C22 | semidirect |
| 135. C173 | #3136 | semidirect |
| 147. #405 | D173 | semidirect |
| 175. #97 | C2×D173 | semidirect |
| 176. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012119 | 2 |
| #26012060 | 2 |
| #26011856 | 2 |
| #26011851 | 2 |
| #26011846 | 2 |
| #26011838 | 2 |
| #26011497 | 2 |
| #26011493 | 2 |
| #26011488 | 2 |
| C2×#19149601 | 2 |
| #405×C173 | 2 |
| #3136 | 173 |