Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 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 |
|---|---|---|
| 2. C4⋊Q8×D173 | C2 | semidirect |
| 3. #26011896 | C2 | semidirect |
| 4. #26011894 | C2 | semidirect |
| 5. #26011837 | C2 | semidirect |
| 6. #26011803 | C2 | semidirect |
| 7. #26011769 | C2 | semidirect |
| 8. #26011542 | C2 | semidirect |
| 9. #486×C173 | C2 | semidirect |
| 113. C173 | #3226 | semidirect |
| 120. #486 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012039 | 2 |
| C4⋊Q8×D173 | 2 |
| #26011896 | 2 |
| #26011894 | 2 |
| #26011837 | 2 |
| #26011803 | 2 |
| #26011769 | 2 |
| #26011542 | 2 |
| #486×C173 | 2 |
| #3226 | 173 |