Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26011862 | C2 | semidirect |
| 4. #26011840 | C2 | semidirect |
| 5. #26011697 | C2 | semidirect |
| 6. #26011696 | C2 | semidirect |
| 7. #26011693 | C2 | semidirect |
| 8. #26011631 | C2 | semidirect |
| 9. #26011628 | C2 | semidirect |
| 10. #26011543 | C2 | semidirect |
| 11. #461×C173 | C2 | semidirect |
| 107. C4×D173 | SD16 | semidirect |
| 148. C173 | #3206 | semidirect |
| 157. #461 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012038 | 2 |
| C4⋊Q8×D173 | 2 |
| #26011862 | 2 |
| #26011840 | 2 |
| #26011697 | 2 |
| #26011696 | 2 |
| #26011693 | 2 |
| #26011631 | 2 |
| #26011628 | 2 |
| #26011543 | 2 |
| #461×C173 | 2 |
| #3206 | 173 |