Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26011829 | C2 | semidirect |
| 3. #26011783 | C2 | semidirect |
| 4. #26011778 | C2 | semidirect |
| 5. #26011698 | C2 | semidirect |
| 6. #26011693 | C2 | semidirect |
| 8. #26011596 | C2 | semidirect |
| 9. #26011589 | C2 | semidirect |
| 10. #26011548 | C2 | semidirect |
| 11. #533×C173 | C2 | semidirect |
| 136. C173 | #3116 | semidirect |
| 138. #533 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14583826 | 2 |
| #26011829 | 2 |
| #26011783 | 2 |
| #26011778 | 2 |
| #26011698 | 2 |
| #26011693 | 2 |
| #26011651 | 2 |
| #26011596 | 2 |
| #26011589 | 2 |
| #26011548 | 2 |
| #533×C173 | 2 |
| #3116 | 173 |