Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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. #26012025 | C2 | semidirect |
| 2. #26011883 | C2 | semidirect |
| 3. #26011878 | C2 | semidirect |
| 4. #26011859 | C2 | semidirect |
| 5. #26011855 | C2 | semidirect |
| 6. #26011710 | C2 | semidirect |
| 7. #26011703 | C2 | semidirect |
| 8. #26011653 | C2 | semidirect |
| 9. #26011636 | C2 | semidirect |
| 10. #26011548 | C2 | semidirect |
| 11. #532×C173 | C2 | semidirect |
| 140. C173 | #3219 | semidirect |
| 142. #532 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012025 | 2 |
| #26011883 | 2 |
| #26011878 | 2 |
| #26011859 | 2 |
| #26011855 | 2 |
| #26011710 | 2 |
| #26011703 | 2 |
| #26011653 | 2 |
| #26011636 | 2 |
| #26011548 | 2 |
| #532×C173 | 2 |
| #3219 | 173 |