Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
440 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 249 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. #26011539 | C2 | semidirect |
| 4. C2×#19149614 | C2 | semidirect |
| 51. C173 | #2916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012258 | 2 |
| C2×#19149686 | 2 |
| #26011539 | 2 |
| C2×#19149614 | 2 |
| #568×C173 | 2 |
| #2916 | 173 |