Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24906027 | C2 | semidirect |
| 5. #24905361 | C2 | semidirect |
| 6. #24905345 | C2 | semidirect |
| 7. C83×#1531 | C2 | semidirect |
| 9. #19128107 | C4 | semidirect |
| 10. #19128093 | C4 | semidirect |
| 11. #19128069 | C4 | semidirect |
| 12. #19128063 | C4 | semidirect |
| 201. #1531 | D83 | semidirect |
| 206. C83 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918166 | 2 |
| #24916457 | 2 |
| #24906027 | 2 |
| #24906002 | 2 |
| #24905361 | 2 |
| #24905345 | 2 |
| C83×#1531 | 2 |
| #9431 | 83 |