Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
436 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 93 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. #24908404 | C2 | semidirect |
| 5. #24905361 | C2 | semidirect |
| 6. #24905314 | C2 | semidirect |
| 7. C83×#1491 | C2 | semidirect |
| 211. #1491 | D83 | semidirect |
| 214. C83 | #9051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917543 | 2 |
| #24916604 | 2 |
| #24908404 | 2 |
| #24906052 | 2 |
| #24905361 | 2 |
| #24905314 | 2 |
| C83×#1491 | 2 |
| #9051 | 83 |