Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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. #26012226 | C2 | semidirect |
| 2. #26012198 | C2 | semidirect |
| 3. #26011847 | C2 | semidirect |
| 4. #26011838 | C2 | semidirect |
| 5. #26011790 | C2 | semidirect |
| 6. #26011786 | C2 | semidirect |
| 7. #26011708 | C2 | semidirect |
| 9. C8×Dic346 | C2 | semidirect |
| 10. #26011571 | C2 | semidirect |
| 11. C4×SD16×C173 | C2 | semidirect |
| 122. C173 | #3361 | semidirect |
| 133. C4×SD16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012226 | 2 |
| #26012198 | 2 |
| #26011847 | 2 |
| #26011838 | 2 |
| #26011790 | 2 |
| #26011786 | 2 |
| #26011708 | 2 |
| #26011686 | 2 |
| C8×Dic346 | 2 |
| #26011571 | 2 |
| C4×SD16×C173 | 2 |
| #3361 | 173 |