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. #26011748 | C2 | semidirect |
| 5. #26011747 | C2 | semidirect |
| 6. #26011733 | C2 | semidirect |
| 7. #26011732 | C2 | semidirect |
| 8. #26011729 | C2 | semidirect |
| 9. #26011528 | C2 | semidirect |
| 10. #26011498 | C2 | semidirect |
| 11. #467×C173 | C2 | semidirect |
| 137. C173 | #3059 | semidirect |
| 147. #467 | 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×#19149685 | 2 |
| #26012064 | 2 |
| #26011748 | 2 |
| #26011747 | 2 |
| #26011733 | 2 |
| #26011732 | 2 |
| #26011729 | 2 |
| #26011528 | 2 |
| #26011498 | 2 |
| #467×C173 | 2 |
| #3059 | 173 |