Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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. #24916074 | C2 | semidirect |
| 2. #24909675 | C2 | semidirect |
| 3. #24909235 | C2 | semidirect |
| 4. C2×#19127514 | C2 | semidirect |
| 5. #24909084 | C2 | semidirect |
| 10. #19127750 | C22 | semidirect |
| 13. #19127523 | C22 | semidirect |
| 15. #19127483 | C22 | semidirect |
| 137. C83 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916074 | 2 |
| #24909675 | 2 |
| #24909235 | 2 |
| C2×#19127514 | 2 |
| #24909084 | 2 |
| C83×#3058 | 2 |
| #33657 | 83 |