Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#19149711 | C2 | semidirect |
| 3. C4×Q8×D173 | C2 | semidirect |
| 4. #26011716 | C2 | semidirect |
| 5. #26011715 | C2 | semidirect |
| 6. #26011698 | C2 | semidirect |
| 7. #26011692 | C2 | semidirect |
| 8. #26011691 | C2 | semidirect |
| 9. #26011513 | C2 | semidirect |
| 10. #26011491 | C2 | semidirect |
| 11. #462×C173 | C2 | semidirect |
| 49. Q8×D173 | D4 | semidirect |
| 133. C4×C173 | #137 | semidirect |
| 146. C173 | #3037 | semidirect |
| 154. #462 | D173 | semidirect |
| 285. C4 | #19149711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149711 | 2 |
| #26012042 | 2 |
| C4×Q8×D173 | 2 |
| #26011716 | 2 |
| #26011715 | 2 |
| #26011698 | 2 |
| #26011692 | 2 |
| #26011691 | 2 |
| #26011513 | 2 |
| #26011491 | 2 |
| #462×C173 | 2 |
| #3037 | 173 |