Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012046 | C2 | semidirect |
| 3. #26011847 | C2 | semidirect |
| 4. #26011841 | C2 | semidirect |
| 5. #26011839 | C2 | semidirect |
| 6. #26011838 | C2 | semidirect |
| 7. #26011486 | C2 | semidirect |
| 8. C4×C8×D173 | C2 | semidirect |
| 9. #487×C173 | C2 | semidirect |
| 111. C173 | #3131 | semidirect |
| 117. #487 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012046 | 2 |
| #26012042 | 2 |
| #26011847 | 2 |
| #26011841 | 2 |
| #26011839 | 2 |
| #26011838 | 2 |
| #26011486 | 2 |
| C4×C8×D173 | 2 |
| #487×C173 | 2 |
| #3131 | 173 |