Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. C2×#19149670 | C2 | semidirect |
| 3. #26011858 | C2 | semidirect |
| 4. #26011854 | C2 | semidirect |
| 5. #26011847 | C2 | semidirect |
| 6. #26011844 | C2 | semidirect |
| 7. #26011493 | C2 | semidirect |
| 8. #26011492 | C2 | semidirect |
| 9. #26011490 | C2 | semidirect |
| 10. M16×Dic173 | C2 | semidirect |
| 11. #417×C173 | C2 | semidirect |
| 146. C173 | #3142 | semidirect |
| 157. #417 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012037 | 2 |
| C2×#19149670 | 2 |
| #26011858 | 2 |
| #26011854 | 2 |
| #26011847 | 2 |
| #26011844 | 2 |
| #26011493 | 2 |
| #26011492 | 2 |
| #26011490 | 2 |
| M16×Dic173 | 2 |
| #417×C173 | 2 |
| #3142 | 173 |