Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012026 | C2 | semidirect |
| 2. #26011875 | C2 | semidirect |
| 3. #26011848 | C2 | semidirect |
| 4. #26011750 | C2 | semidirect |
| 6. #26011738 | C2 | semidirect |
| 7. #26011602 | C2 | semidirect |
| 8. #26011597 | C2 | semidirect |
| 9. #26011590 | C2 | semidirect |
| 10. C4×#14583809 | C2 | semidirect |
| 11. #499×C173 | C2 | semidirect |
| 109. C173 | #3183 | semidirect |
| 112. #499 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012026 | 2 |
| #26011875 | 2 |
| #26011848 | 2 |
| #26011750 | 2 |
| #26011745 | 2 |
| #26011738 | 2 |
| #26011602 | 2 |
| #26011597 | 2 |
| #26011590 | 2 |
| C4×#14583809 | 2 |
| #499×C173 | 2 |
| #3183 | 173 |