Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 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. #26012067 | C2 | semidirect |
| 2. #26011878 | C2 | semidirect |
| 3. #26011863 | C2 | semidirect |
| 4. #26011861 | C2 | semidirect |
| 5. #26011848 | C2 | semidirect |
| 6. #26011706 | C2 | semidirect |
| 7. #26011696 | C2 | semidirect |
| 8. #26011634 | C2 | semidirect |
| 9. #26011629 | C2 | semidirect |
| 10. #26011552 | C2 | semidirect |
| 11. #540×C173 | C2 | semidirect |
| 120. C173 | #3221 | semidirect |
| 122. #540 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012067 | 2 |
| #26011878 | 2 |
| #26011863 | 2 |
| #26011861 | 2 |
| #26011848 | 2 |
| #26011706 | 2 |
| #26011696 | 2 |
| #26011634 | 2 |
| #26011629 | 2 |
| #26011552 | 2 |
| #540×C173 | 2 |
| #3221 | 173 |