Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
376 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26011801 | C2 | semidirect |
| 4. #26011797 | C2 | semidirect |
| 5. #26011785 | C2 | semidirect |
| 6. #26011775 | C2 | semidirect |
| 47. C2×Dic346 | Q8 | semidirect |
| 129. C173 | #3078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012044 | 2 |
| C2×#19149644 | 2 |
| #26011801 | 2 |
| #26011797 | 2 |
| #26011785 | 2 |
| #26011775 | 2 |
| #26011531 | 2 |
| #26011514 | 2 |
| #26011501 | 2 |
| #26011499 | 2 |
| #428×C173 | 2 |
| #3078 | 173 |