Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×Dic692 | C2 | semidirect |
| 3. #26011749 | C2 | semidirect |
| 4. #26011732 | C2 | semidirect |
| 5. #26011529 | C2 | semidirect |
| 6. #26011501 | C2 | semidirect |
| 88. C173 | #3059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic692 | 2 |
| #26012062 | 2 |
| #26011749 | 2 |
| #26011732 | 2 |
| #26011529 | 2 |
| #26011501 | 2 |
| C2×#131×C173 | 2 |
| #3059 | 173 |