Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 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 |
|---|---|---|
| 1. #26011895 | C2 | semidirect |
| 3. #26011293 | C2 | semidirect |
| 4. #26011292 | C2 | semidirect |
| 5. #26011291 | C2 | semidirect |
| 6. C16×Dic173 | C2 | semidirect |
| 7. #357×C173 | C2 | semidirect |
| 72. C173 | #2240 | semidirect |
| 79. #357 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011895 | 2 |
| #26011866 | 2 |
| #26011293 | 2 |
| #26011292 | 2 |
| #26011291 | 2 |
| C16×Dic173 | 2 |
| #357×C173 | 2 |
| #2240 | 173 |