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 |
|---|---|---|
| 2. #24909677 | C2 | semidirect |
| 3. #24909237 | C2 | semidirect |
| 4. C2×#19127513 | C2 | semidirect |
| 5. #24909084 | C2 | semidirect |
| 6. C83×#2916 | C2 | semidirect |
| 14. #19127525 | C22 | semidirect |
| 16. #19127483 | C22 | semidirect |
| 20. #430×C83 | C22 | semidirect |
| 132. #2916 | D83 | semidirect |
| 137. C83 | #33657 | semidirect |
| 146. #430 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917111 | 2 |
| #24909677 | 2 |
| #24909237 | 2 |
| C2×#19127513 | 2 |
| #24909084 | 2 |
| C83×#2916 | 2 |
| #33657 | 83 |