Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #26011531 | C2 | semidirect |
| 4. #26011530 | C2 | semidirect |
| 5. #26011529 | C2 | semidirect |
| 6. #26011526 | C2 | semidirect |
| 7. #106×D173 | C2 | semidirect |
| 8. C2×#106×C173 | C2 | semidirect |
| 10. #19149685 | C4 | semidirect |
| 36. #14583810 | C2×C4 | semidirect |
| 37. #14583809 | C2×C4 | semidirect |
| 39. C8×D173 | C2×C4 | semidirect |
| 49. C2×C8×C173 | C2×C4 | semidirect |
| 90. C173 | #2912 | semidirect |
| 99. C2×#106 | D173 | semidirect |
| 133. C2×C8 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149685 | 2 |
| #26011972 | 2 |
| #26011531 | 2 |
| #26011530 | 2 |
| #26011529 | 2 |
| #26011526 | 2 |
| #106×D173 | 2 |
| C2×#106×C173 | 2 |
| #2912 | 173 |