Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
434 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 434 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. #26012039 | C2 | semidirect |
| 2. #26012038 | C2 | semidirect |
| 3. #26011879 | C2 | semidirect |
| 4. #26011849 | C2 | semidirect |
| 5. #26011697 | C2 | semidirect |
| 6. #26011696 | C2 | semidirect |
| 7. #26011683 | C2 | semidirect |
| 8. #26011637 | C2 | semidirect |
| 9. #26011633 | C2 | semidirect |
| 10. #26011547 | C2 | semidirect |
| 11. #459×C173 | C2 | semidirect |
| 153. C173 | #3214 | semidirect |
| 162. #459 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012039 | 2 |
| #26012038 | 2 |
| #26011879 | 2 |
| #26011849 | 2 |
| #26011697 | 2 |
| #26011696 | 2 |
| #26011683 | 2 |
| #26011637 | 2 |
| #26011633 | 2 |
| #26011547 | 2 |
| #459×C173 | 2 |
| #3214 | 173 |