Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149726 | C2 | semidirect |
| 2. C2×#19149712 | C2 | semidirect |
| 3. C2×#19149699 | C2 | semidirect |
| 4. #26012072 | C2 | semidirect |
| 5. #26011654 | C2 | semidirect |
| 6. #26011648 | C2 | semidirect |
| 7. #26011637 | C2 | semidirect |
| 8. #26011631 | C2 | semidirect |
| 9. C2×#19149602 | C2 | semidirect |
| 10. #26011459 | C2 | semidirect |
| 11. #417×C173 | C2 | semidirect |
| 58. C2×Dic346 | D4 | semidirect |
| 87. #41×C173 | D4 | semidirect |
| 169. C173 | #3013 | semidirect |
| 179. #417 | D173 | semidirect |
| 224. #41 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149726 | 2 |
| C2×#19149712 | 2 |
| C2×#19149699 | 2 |
| #26012072 | 2 |
| #26011654 | 2 |
| #26011648 | 2 |
| #26011637 | 2 |
| #26011631 | 2 |
| C2×#19149602 | 2 |
| #26011459 | 2 |
| #417×C173 | 2 |
| #3013 | 173 |