Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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×Q16×D173 | C2 | semidirect |
| 4. #26011750 | C2 | semidirect |
| 5. #26011749 | C2 | semidirect |
| 6. #26011746 | C2 | semidirect |
| 7. #26011731 | C2 | semidirect |
| 8. #26011730 | C2 | semidirect |
| 9. #26011526 | C2 | semidirect |
| 10. #26011498 | C2 | semidirect |
| 11. #470×C173 | C2 | semidirect |
| 133. C173 | #3059 | semidirect |
| 141. #470 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D173 | 2 |
| C2×#19149687 | 2 |
| #26012064 | 2 |
| #26011750 | 2 |
| #26011749 | 2 |
| #26011746 | 2 |
| #26011731 | 2 |
| #26011730 | 2 |
| #26011526 | 2 |
| #26011498 | 2 |
| #470×C173 | 2 |
| #3059 | 173 |