Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 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. #26012202 | C2 | semidirect |
| 3. #26011834 | C2 | semidirect |
| 4. #26011806 | C2 | semidirect |
| 5. #26011783 | C2 | semidirect |
| 6. #26011778 | C2 | semidirect |
| 7. #26011738 | C2 | semidirect |
| 8. C4×#14583815 | C2 | semidirect |
| 9. #26011570 | C2 | semidirect |
| 10. #26011532 | C2 | semidirect |
| 11. #500×C173 | C2 | semidirect |
| 121. C173 | #3357 | semidirect |
| 125. #500 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012207 | 2 |
| #26012202 | 2 |
| #26011834 | 2 |
| #26011806 | 2 |
| #26011783 | 2 |
| #26011778 | 2 |
| #26011738 | 2 |
| C4×#14583815 | 2 |
| #26011570 | 2 |
| #26011532 | 2 |
| #500×C173 | 2 |
| #3357 | 173 |