Finite Group DatabasebetaFinite Group DatabasebetaOrder 21568.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24924954 | C2 | semidirect |
| 2. #24924952 | C2 | semidirect |
| 3. #24924949 | C2 | semidirect |
| 4. #24924945 | C2 | semidirect |
| 5. #24924944 | C2 | semidirect |
| 6. #24924941 | C2 | semidirect |
| 7. #24924937 | C2 | semidirect |
| 9. C4×Dic674 | C2 | semidirect |
| 10. C4×D1348 | C2 | semidirect |
| 11. C4×C22⋊D337 | C2 | semidirect |
| 12. C4×C22⋊D337 | C2 | semidirect |
| 13. #24924916 | C2 | semidirect |
| 14. C42×D337 | C2 | semidirect |
| 15. #117×C337 | C2 | semidirect |
| 103. C337 | #529 | semidirect |
| 118. #117 | D337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924954 | 2 |
| #24924952 | 2 |
| #24924949 | 2 |
| #24924945 | 2 |
| #24924944 | 2 |
| #24924941 | 2 |
| #24924937 | 2 |
| #24924932 | 2 |
| C4×Dic674 | 2 |
| C4×D1348 | 2 |
| C4×C22⋊D337 | 2 |
| #24924916 | 2 |
| C42×D337 | 2 |
| #117×C337 | 2 |
| #529 | 337 |