Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26012022 | C2 | semidirect |
| 2. C2×#19149668 | C2 | semidirect |
| 3. #26011872 | C2 | semidirect |
| 4. #26011847 | C2 | semidirect |
| 5. #26011716 | C2 | semidirect |
| 6. #26011708 | C2 | semidirect |
| 7. #26011647 | C2 | semidirect |
| 8. #26011644 | C2 | semidirect |
| 10. #26011541 | C2 | semidirect |
| 11. #448×C173 | C2 | semidirect |
| 13. C2×#14583816 | C22 | semidirect |
| 17. #19149670 | C22 | semidirect |
| 22. #19149666 | C22 | semidirect |
| 25. #19149644 | C22 | semidirect |
| 27. D4×Dic173 | C22 | semidirect |
| 32. #19149608 | C22 | semidirect |
| 33. #19149603 | C22 | semidirect |
| 37. C8×Dic173 | C22 | semidirect |
| 39. C2×SD16×C173 | C22 | semidirect |
| 41. #103×C173 | C22 | semidirect |
| 143. C173 | #3211 | semidirect |
| 153. #448 | D173 | semidirect |
| 160. C2×SD16 | C2×D173 | semidirect |
| 181. #103 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012022 | 2 |
| C2×#19149668 | 2 |
| #26011872 | 2 |
| #26011847 | 2 |
| #26011716 | 2 |
| #26011708 | 2 |
| #26011647 | 2 |
| #26011644 | 2 |
| #26011624 | 2 |
| #26011541 | 2 |
| #448×C173 | 2 |
| #3211 | 173 |