Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. C2×#19149644 | C2 | semidirect |
| 4. #26011797 | C2 | semidirect |
| 5. #26011716 | C2 | semidirect |
| 6. #26011646 | C2 | semidirect |
| 8. #26011595 | C2 | semidirect |
| 9. #26011590 | C2 | semidirect |
| 10. #26011545 | C2 | semidirect |
| 11. #484×C173 | C2 | semidirect |
| 131. C173 | #3117 | semidirect |
| 135. #484 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012027 | 2 |
| C2×#19149644 | 2 |
| #26011809 | 2 |
| #26011797 | 2 |
| #26011716 | 2 |
| #26011646 | 2 |
| #26011632 | 2 |
| #26011595 | 2 |
| #26011590 | 2 |
| #26011545 | 2 |
| #484×C173 | 2 |
| #3117 | 173 |