Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
688 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 169 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 |
|---|---|---|
| 1. C2×#19149662 | C2 | semidirect |
| 3. C22×C4×Dic173 | C2 | semidirect |
| 4. #26011391 | C2 | semidirect |
| 5. #26011386 | C2 | semidirect |
| 6. #26011385 | C2 | semidirect |
| 7. #26011381 | C2 | semidirect |
| 8. #26011371 | C2 | semidirect |
| 9. #26011368 | C2 | semidirect |
| 10. #26011349 | C2 | semidirect |
| 11. C2×#123×C173 | C2 | semidirect |
| 72. C22×C4×C173 | D4 | semidirect |
| 150. Dic173 | #123 | semidirect |
| 159. C173 | #2854 | semidirect |
| 162. C2×#123 | D173 | semidirect |
| 221. C22×C4 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149662 | 2 |
| C2×#19149651 | 2 |
| C22×C4×Dic173 | 2 |
| #26011391 | 2 |
| #26011386 | 2 |
| #26011385 | 2 |
| #26011381 | 2 |
| #26011371 | 2 |
| #26011368 | 2 |
| #26011349 | 2 |
| C2×#123×C173 | 2 |
| #2854 | 173 |