Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #26011835 | C2 | semidirect |
| 4. #26011823 | C2 | semidirect |
| 5. #26011783 | C2 | semidirect |
| 6. #26011773 | C2 | semidirect |
| 7. #26011750 | C2 | semidirect |
| 8. C4×Dic692 | C2 | semidirect |
| 10. #26011530 | C2 | semidirect |
| 11. #498×C173 | C2 | semidirect |
| 116. C173 | #3356 | semidirect |
| 120. #498 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012215 | 2 |
| #26012202 | 2 |
| #26011835 | 2 |
| #26011823 | 2 |
| #26011783 | 2 |
| #26011773 | 2 |
| #26011750 | 2 |
| C4×Dic692 | 2 |
| #26011570 | 2 |
| #26011530 | 2 |
| #498×C173 | 2 |
| #3356 | 173 |