Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 135 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×#19149712 | C2 | semidirect |
| 2. C2×#19149709 | C2 | semidirect |
| 4. C2×#19149644 | C2 | semidirect |
| 5. #26011716 | C2 | semidirect |
| 6. #26011712 | C2 | semidirect |
| 7. #26011700 | C2 | semidirect |
| 8. #26011690 | C2 | semidirect |
| 9. #26011514 | C2 | semidirect |
| 10. #26011490 | C2 | semidirect |
| 11. #417×C173 | C2 | semidirect |
| 49. C2×Dic346 | D4 | semidirect |
| 150. Dic173 | #137 | semidirect |
| 157. C173 | #3037 | semidirect |
| 169. #417 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149712 | 2 |
| C2×#19149709 | 2 |
| #26012037 | 2 |
| C2×#19149644 | 2 |
| #26011716 | 2 |
| #26011712 | 2 |
| #26011700 | 2 |
| #26011690 | 2 |
| #26011514 | 2 |
| #26011490 | 2 |
| #417×C173 | 2 |
| #3037 | 173 |