Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 2. #24905972 | C2 | semidirect |
| 3. #24905971 | C2 | semidirect |
| 4. #24905933 | C2 | semidirect |
| 5. #24905326 | C2 | semidirect |
| 6. #24905291 | C2 | semidirect |
| 7. C83×#2981 | C2 | semidirect |
| 9. #19128077 | C4 | semidirect |
| 10. #19128073 | C4 | semidirect |
| 11. #19128053 | C4 | semidirect |
| 12. #19128049 | C4 | semidirect |
| 180. #2981 | D83 | semidirect |
| 186. C83 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918392 | 2 |
| #24905972 | 2 |
| #24905971 | 2 |
| #24905933 | 2 |
| #24905326 | 2 |
| #24905291 | 2 |
| C83×#2981 | 2 |
| #9281 | 83 |