Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
422 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 83 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. C22⋊C16×D83 | C2 | semidirect |
| 3. #24907487 | C2 | semidirect |
| 4. #24905476 | C2 | semidirect |
| 5. #24905474 | C2 | semidirect |
| 6. #24905472 | C2 | semidirect |
| 7. C83×#1347 | C2 | semidirect |
| 8. C2×#14581811 | C4 | semidirect |
| 12. #19127943 | C4 | semidirect |
| 14. #19127934 | C4 | semidirect |
| 17. #19127738 | C4 | semidirect |
| 197. #1347 | D83 | semidirect |
| 198. C83 | #11885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917042 | 2 |
| C22⋊C16×D83 | 2 |
| #24907487 | 2 |
| #24905476 | 2 |
| #24905474 | 2 |
| #24905472 | 2 |
| C83×#1347 | 2 |
| #11885 | 83 |