Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 2. C2×#19149708 | C2 | semidirect |
| 4. C4⋊Q8×D173 | C2 | semidirect |
| 5. #26011886 | C2 | semidirect |
| 6. #26011885 | C2 | semidirect |
| 7. #26011883 | C2 | semidirect |
| 8. #26011869 | C2 | semidirect |
| 9. #26011862 | C2 | semidirect |
| 10. #26011443 | C2 | semidirect |
| 11. #497×C173 | C2 | semidirect |
| 63. #14583809 | D4 | semidirect |
| 124. Dic173 | #137 | semidirect |
| 130. C173 | #3152 | semidirect |
| 139. #497 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149711 | 2 |
| C2×#19149708 | 2 |
| #26012040 | 2 |
| C4⋊Q8×D173 | 2 |
| #26011886 | 2 |
| #26011885 | 2 |
| #26011883 | 2 |
| #26011869 | 2 |
| #26011862 | 2 |
| #26011443 | 2 |
| #497×C173 | 2 |
| #3152 | 173 |