Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26012039 | C2 | semidirect |
| 2. #26012026 | C2 | semidirect |
| 3. #26011901 | C2 | semidirect |
| 4. #26011878 | C2 | semidirect |
| 5. #26011851 | C2 | semidirect |
| 6. #26011743 | C2 | semidirect |
| 7. #26011736 | C2 | semidirect |
| 8. #26011582 | C2 | semidirect |
| 9. #26011571 | C2 | semidirect |
| 10. #26011443 | C2 | semidirect |
| 11. #490×C173 | C2 | semidirect |
| 99. #13063436 | #41 | semidirect |
| 137. C173 | #3171 | semidirect |
| 143. #490 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012039 | 2 |
| #26012026 | 2 |
| #26011901 | 2 |
| #26011878 | 2 |
| #26011851 | 2 |
| #26011743 | 2 |
| #26011736 | 2 |
| #26011582 | 2 |
| #26011571 | 2 |
| #26011443 | 2 |
| #490×C173 | 2 |
| #3171 | 173 |