Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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. #26012094 | C2 | semidirect |
| 2. #26011891 | C2 | semidirect |
| 3. #26011866 | C2 | semidirect |
| 4. #26011854 | C2 | semidirect |
| 5. #26011744 | C2 | semidirect |
| 6. #26011725 | C2 | semidirect |
| 7. #26011603 | C2 | semidirect |
| 8. #26011602 | C2 | semidirect |
| 9. #26011571 | C2 | semidirect |
| 10. #26011449 | C2 | semidirect |
| 11. #469×C173 | C2 | semidirect |
| 115. C173 | #3176 | semidirect |
| 122. #469 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012094 | 2 |
| #26011891 | 2 |
| #26011866 | 2 |
| #26011854 | 2 |
| #26011744 | 2 |
| #26011725 | 2 |
| #26011603 | 2 |
| #26011602 | 2 |
| #26011571 | 2 |
| #26011449 | 2 |
| #469×C173 | 2 |
| #3176 | 173 |