Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26011829 | C2 | semidirect |
| 3. #26011829 | C2 | semidirect |
| 4. #26011824 | C2 | semidirect |
| 5. #26011819 | C2 | semidirect |
| 6. #26011534 | C2 | semidirect |
| 7. #26011527 | C2 | semidirect |
| 8. #26011500 | C2 | semidirect |
| 9. C2×#19149603 | C2 | semidirect |
| 126. C173 | #3097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011974 | 2 |
| #26011829 | 2 |
| #26011824 | 2 |
| #26011819 | 2 |
| #26011534 | 2 |
| #26011527 | 2 |
| #26011500 | 2 |
| C2×#19149603 | 2 |
| #26011458 | 2 |
| #536×C173 | 2 |
| #3097 | 173 |