Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
704 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 704 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 |
|---|---|---|
| 2. #26012258 | C2 | semidirect |
| 3. #26011473 | C2 | semidirect |
| 4. C2×#19149597 | C2 | semidirect |
| 5. #568×C173 | C2 | semidirect |
| 74. C173 | #2889 | semidirect |
| 78. #568 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149726 | 2 |
| #26012258 | 2 |
| #26011473 | 2 |
| C2×#19149597 | 2 |
| #568×C173 | 2 |
| #2889 | 173 |