Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 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. #26011313 | C2 | semidirect |
| 3. #26011312 | C2 | semidirect |
| 5. #498×C173 | C2 | semidirect |
| 16. Dic692 | Q8 | semidirect |
| 18. D1384 | Q8 | semidirect |
| 52. C173 | #2230 | semidirect |
| 54. #498 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011609 | 2 |
| #26011313 | 2 |
| #26011312 | 2 |
| #26011300 | 2 |
| #498×C173 | 2 |
| #2230 | 173 |