Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 3. #26011598 | C2 | semidirect |
| 4. #26011315 | C2 | semidirect |
| 6. #26011268 | C2 | semidirect |
| 7. #362×C173 | C2 | semidirect |
| 11. #19149625 | C4 | semidirect |
| 12. #19149622 | C4 | semidirect |
| 64. C173 | #2180 | semidirect |
| 70. #362 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011932 | 2 |
| #26011612 | 2 |
| #26011598 | 2 |
| #26011315 | 2 |
| #26011302 | 2 |
| #26011268 | 2 |
| #362×C173 | 2 |
| #2180 | 173 |