Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26012191 | C2 | semidirect |
| 2. #26011893 | C2 | semidirect |
| 3. #26011813 | C2 | semidirect |
| 4. #26011803 | C2 | semidirect |
| 5. #26011791 | C2 | semidirect |
| 6. #26011741 | C2 | semidirect |
| 7. #26011570 | C2 | semidirect |
| 8. #26011532 | C2 | semidirect |
| 9. C4×D8×C173 | C2 | semidirect |
| 102. C173 | #3355 | semidirect |
| 110. C4×D8 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012191 | 2 |
| #26011893 | 2 |
| #26011813 | 2 |
| #26011803 | 2 |
| #26011791 | 2 |
| #26011741 | 2 |
| #26011570 | 2 |
| #26011532 | 2 |
| C4×D8×C173 | 2 |
| #3355 | 173 |