Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19149670 | C2 | semidirect |
| 3. #26011801 | C2 | semidirect |
| 4. #26011797 | C2 | semidirect |
| 5. #26011794 | C2 | semidirect |
| 6. #26011790 | C2 | semidirect |
| 7. #26011534 | C2 | semidirect |
| 8. #26011514 | C2 | semidirect |
| 11. #428×C173 | C2 | semidirect |
| 135. C173 | #3080 | semidirect |
| 144. #428 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149670 | 2 |
| #26011959 | 2 |
| #26011801 | 2 |
| #26011797 | 2 |
| #26011794 | 2 |
| #26011790 | 2 |
| #26011534 | 2 |
| #26011514 | 2 |
| #26011493 | 2 |
| #26011490 | 2 |
| #428×C173 | 2 |
| #3080 | 173 |