Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
222 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 75 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. #26011518 | C2 | semidirect |
| 5. C2×#19149590 | C2 | semidirect |
| 6. #26011255 | C2 | semidirect |
| 7. #339×C173 | C2 | semidirect |
| 14. #19149602 | C4 | semidirect |
| 15. #19149599 | C4 | semidirect |
| 90. C173 | #1938 | semidirect |
| 98. #339 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011518 | 2 |
| C2×#19149607 | 2 |
| #26011485 | 2 |
| #26011459 | 2 |
| C2×#19149590 | 2 |
| #26011255 | 2 |
| #339×C173 | 2 |
| #1938 | 173 |