Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26011888 | C2 | semidirect |
| 3. #26011869 | C2 | semidirect |
| 4. #26011840 | C2 | semidirect |
| 7. #26011598 | C2 | semidirect |
| 8. #26011597 | C2 | semidirect |
| 9. #26011595 | C2 | semidirect |
| 105. C173 | #3185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012043 | 2 |
| #26011888 | 2 |
| #26011869 | 2 |
| #26011840 | 2 |
| #26011749 | 2 |
| #26011747 | 2 |
| #26011598 | 2 |
| #26011597 | 2 |
| #26011595 | 2 |
| M16×Dic173 | 2 |
| #470×C173 | 2 |
| #3185 | 173 |