Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 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 |
|---|---|---|
| 2. #26012067 | C2 | semidirect |
| 3. C2×#19149667 | C2 | semidirect |
| 4. C2×#19149607 | C2 | semidirect |
| 5. #26011495 | C2 | semidirect |
| 6. C2×#19149597 | C2 | semidirect |
| 7. #339×C173 | C2 | semidirect |
| 130. C173 | #2003 | semidirect |
| 138. #339 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149707 | 2 |
| #26012067 | 2 |
| C2×#19149667 | 2 |
| C2×#19149607 | 2 |
| #26011495 | 2 |
| C2×#19149597 | 2 |
| #339×C173 | 2 |
| #2003 | 173 |