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. #26012214 | C2 | semidirect |
| 3. #26011841 | C2 | semidirect |
| 4. #26011831 | C2 | semidirect |
| 5. #26011772 | C2 | semidirect |
| 6. #26011729 | C2 | semidirect |
| 7. #26011652 | C2 | semidirect |
| 8. C4×#14583813 | C2 | semidirect |
| 9. #26011556 | C2 | semidirect |
| 10. #26011486 | C2 | semidirect |
| 11. #462×C173 | C2 | semidirect |
| 125. C173 | #3302 | semidirect |
| 133. #462 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012214 | 2 |
| #26012144 | 2 |
| #26011841 | 2 |
| #26011831 | 2 |
| #26011772 | 2 |
| #26011729 | 2 |
| #26011652 | 2 |
| C4×#14583813 | 2 |
| #26011556 | 2 |
| #26011486 | 2 |
| #462×C173 | 2 |
| #3302 | 173 |