Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26012119 | C2 | semidirect |
| 3. #26011860 | C2 | semidirect |
| 4. #26011851 | C2 | semidirect |
| 5. #26011846 | C2 | semidirect |
| 6. #26011842 | C2 | semidirect |
| 7. #26011501 | C2 | semidirect |
| 10. C2×#19149604 | C2 | semidirect |
| 11. #405×C173 | C2 | semidirect |
| 127. C173 | #3137 | semidirect |
| 139. #405 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012119 | 2 |
| #26012067 | 2 |
| #26011860 | 2 |
| #26011851 | 2 |
| #26011846 | 2 |
| #26011842 | 2 |
| #26011501 | 2 |
| #26011493 | 2 |
| #26011488 | 2 |
| C2×#19149604 | 2 |
| #405×C173 | 2 |
| #3137 | 173 |