Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
532 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 165 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×#19149712 | C2 | semidirect |
| 3. C22×Dic692 | C2 | semidirect |
| 4. #26012067 | C2 | semidirect |
| 5. #26011885 | C2 | semidirect |
| 6. #26011875 | C2 | semidirect |
| 7. #26011871 | C2 | semidirect |
| 8. #405×C173 | C2 | semidirect |
| 96. C173 | #3156 | semidirect |
| 105. #405 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149712 | 2 |
| C2×#19149701 | 2 |
| C22×Dic692 | 2 |
| #26012067 | 2 |
| #26011885 | 2 |
| #26011875 | 2 |
| #26011871 | 2 |
| #405×C173 | 2 |
| #3156 | 173 |