Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 255 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. #26011519 | C2 | semidirect |
| 4. #26011517 | C2 | semidirect |
| 5. #26011514 | C2 | semidirect |
| 6. C2×#19149608 | C2 | semidirect |
| 75. Dic173 | #131 | semidirect |
| 80. C173 | #2906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149686 | 2 |
| #41×Dic173 | 2 |
| #26011519 | 2 |
| #26011517 | 2 |
| #26011514 | 2 |
| C2×#19149608 | 2 |
| C2×#131×C173 | 2 |
| #2906 | 173 |