Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
438 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 85 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. #24916533 | C2 | semidirect |
| 3. #24906166 | C2 | semidirect |
| 4. #24906087 | C2 | semidirect |
| 5. C83⋊#1308 | C2 | semidirect |
| 6. #24905325 | C2 | semidirect |
| 7. C83×#1469 | C2 | semidirect |
| 170. #1469 | D83 | semidirect |
| 173. C83 | #9333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918450 | 2 |
| #24916533 | 2 |
| #24906166 | 2 |
| #24906087 | 2 |
| C83⋊#1308 | 2 |
| #24905325 | 2 |
| C83×#1469 | 2 |
| #9333 | 83 |