Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
726 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 2. #26011974 | C2 | semidirect |
| 3. #26011501 | C2 | semidirect |
| 4. #26011493 | C2 | semidirect |
| 5. #26011488 | C2 | semidirect |
| 6. C2×#19149604 | C2 | semidirect |
| 7. C2×#131×C173 | C2 | semidirect |
| 9. #19149726 | C4 | semidirect |
| 28. #14583826 | C2×C4 | semidirect |
| 32. C2×Dic346 | C2×C4 | semidirect |
| 94. C173 | #2898 | semidirect |
| 97. C2×#131 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149726 | 2 |
| #26011974 | 2 |
| #26011501 | 2 |
| #26011493 | 2 |
| #26011488 | 2 |
| C2×#19149604 | 2 |
| C2×#131×C173 | 2 |
| #2898 | 173 |