Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26012028 | C2 | semidirect |
| 2. #26011891 | C2 | semidirect |
| 3. #26011876 | C2 | semidirect |
| 4. #26011847 | C2 | semidirect |
| 5. #26011746 | C2 | semidirect |
| 7. #26011740 | C2 | semidirect |
| 8. #26011604 | C2 | semidirect |
| 9. #26011589 | C2 | semidirect |
| 10. #26011443 | C2 | semidirect |
| 11. #441×C173 | C2 | semidirect |
| 109. C173 | #3183 | semidirect |
| 119. #441 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012028 | 2 |
| #26011891 | 2 |
| #26011876 | 2 |
| #26011847 | 2 |
| #26011746 | 2 |
| #26011745 | 2 |
| #26011740 | 2 |
| #26011604 | 2 |
| #26011589 | 2 |
| #26011443 | 2 |
| #441×C173 | 2 |
| #3183 | 173 |