Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #24906100 | C2 | semidirect |
| 5. #24905867 | C2 | semidirect |
| 6. #24905332 | C2 | semidirect |
| 7. C83×#1287 | C2 | semidirect |
| 170. #1287 | D83 | semidirect |
| 171. C83 | #9373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918476 | 2 |
| #24916538 | 2 |
| #24906159 | 2 |
| #24906100 | 2 |
| #24905867 | 2 |
| #24905332 | 2 |
| C83×#1287 | 2 |
| #9373 | 83 |