Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
170 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 43 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. #26011929 | C2 | semidirect |
| 2. #26011927 | C2 | semidirect |
| 3. #26011866 | C2 | semidirect |
| 4. #26011607 | C2 | semidirect |
| 5. #26011311 | C2 | semidirect |
| 6. #26011303 | C2 | semidirect |
| 7. #361×C173 | C2 | semidirect |
| 26. Dic692 | D4 | semidirect |
| 30. D1384 | D4 | semidirect |
| 77. C173 | #2213 | semidirect |
| 85. #361 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011929 | 2 |
| #26011927 | 2 |
| #26011866 | 2 |
| #26011607 | 2 |
| #26011311 | 2 |
| #26011303 | 2 |
| #361×C173 | 2 |
| #2213 | 173 |