Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 2. #125×D173 | C2 | semidirect |
| 3. #26011859 | C2 | semidirect |
| 4. #26011857 | C2 | semidirect |
| 5. #26011856 | C2 | semidirect |
| 6. #26011847 | C2 | semidirect |
| 7. #26011491 | C2 | semidirect |
| 8. #26011443 | C2 | semidirect |
| 9. #491×C173 | C2 | semidirect |
| 90. C173 | #3142 | semidirect |
| 95. #491 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012042 | 2 |
| #125×D173 | 2 |
| #26011859 | 2 |
| #26011857 | 2 |
| #26011856 | 2 |
| #26011847 | 2 |
| #26011491 | 2 |
| #26011443 | 2 |
| #491×C173 | 2 |
| #3142 | 173 |