Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012220 | C2 | semidirect |
| 4. #26011841 | C2 | semidirect |
| 5. #26011800 | C2 | semidirect |
| 8. #26011615 | C2 | semidirect |
| 9. Q16×Dic173 | C2 | semidirect |
| 11. #462×C173 | C2 | semidirect |
| 115. C173 | #3364 | semidirect |
| 124. #462 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012220 | 2 |
| #26012215 | 2 |
| #26011847 | 2 |
| #26011841 | 2 |
| #26011800 | 2 |
| #26011772 | 2 |
| #26011715 | 2 |
| #26011615 | 2 |
| Q16×Dic173 | 2 |
| C4×#14583813 | 2 |
| #462×C173 | 2 |
| #3364 | 173 |