Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#19149704 | C2 | semidirect |
| 2. C2×#19149704 | C2 | semidirect |
| 3. #26012258 | C2 | semidirect |
| 4. #26011759 | C2 | semidirect |
| 5. #26011756 | C2 | semidirect |
| 6. #26011539 | C2 | semidirect |
| 7. #26011475 | C2 | semidirect |
| 8. C2×#19149595 | C2 | semidirect |
| 9. #575×C173 | C2 | semidirect |
| 16. C2×#14583813 | C22 | semidirect |
| 18. C2×#14583811 | C22 | semidirect |
| 20. #19149686 | C22 | semidirect |
| 25. #19149614 | C22 | semidirect |
| 26. #19149598 | C22 | semidirect |
| 27. #19149596 | C22 | semidirect |
| 28. #19149595 | C22 | semidirect |
| 32. #137×C173 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C173 | C22 | semidirect |
| 147. C173 | #3068 | semidirect |
| 149. #575 | D173 | semidirect |
| 162. #137 | C2×D173 | semidirect |
| 168. AGL(1,ℤ/8) | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149704 | 2 |
| #26012258 | 2 |
| #26011759 | 2 |
| #26011756 | 2 |
| #26011539 | 2 |
| #26011475 | 2 |
| C2×#19149595 | 2 |
| #575×C173 | 2 |
| #3068 | 173 |