Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
362 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 3. #26011801 | C2 | semidirect |
| 4. #26011797 | C2 | semidirect |
| 5. #26011785 | C2 | semidirect |
| 6. #26011775 | C2 | semidirect |
| 44. C2×Dic346 | Q8 | semidirect |
| 116. C173 | #3082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012119 | 2 |
| #26011968 | 2 |
| #26011801 | 2 |
| #26011797 | 2 |
| #26011785 | 2 |
| #26011775 | 2 |
| #26011534 | 2 |
| #26011517 | 2 |
| #26011499 | 2 |
| C2×#19149604 | 2 |
| #427×C173 | 2 |
| #3082 | 173 |