Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
456 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 103 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. #24916539 | C2 | semidirect |
| 2. #24905971 | C2 | semidirect |
| 3. #24905971 | C2 | semidirect |
| 4. #24905932 | C2 | semidirect |
| 5. #24905325 | C2 | semidirect |
| 6. #24905291 | C2 | semidirect |
| 22. #493×C83 | C4 | semidirect |
| 23. #492×C83 | C4 | semidirect |
| 24. #487×C83 | C4 | semidirect |
| 25. #486×C83 | C4 | semidirect |
| 186. C83 | #9281 | semidirect |
| 189. #493 | Dic83 | semidirect |
| 190. #492 | Dic83 | semidirect |
| 191. #487 | Dic83 | semidirect |
| 192. #486 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916539 | 2 |
| #24905971 | 2 |
| #24905932 | 2 |
| #24905325 | 2 |
| #24905291 | 2 |
| C83×#3207 | 2 |
| #9281 | 83 |