Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26012108 | C2 | semidirect |
| 2. #26011895 | C2 | semidirect |
| 3. #26011874 | C2 | semidirect |
| 4. #26011849 | C2 | semidirect |
| 5. #26011735 | C2 | semidirect |
| 6. #26011732 | C2 | semidirect |
| 7. #26011588 | C2 | semidirect |
| 8. #26011585 | C2 | semidirect |
| 9. D8×Dic173 | C2 | semidirect |
| 10. #26011446 | C2 | semidirect |
| 117. C173 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012108 | 2 |
| #26011895 | 2 |
| #26011874 | 2 |
| #26011849 | 2 |
| #26011735 | 2 |
| #26011732 | 2 |
| #26011588 | 2 |
| #26011585 | 2 |
| D8×Dic173 | 2 |
| #26011446 | 2 |
| #466×C173 | 2 |
| #3175 | 173 |