Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
464 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 127 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. #24909629 | C2 | semidirect |
| 3. #24909626 | C2 | semidirect |
| 6. #24909512 | C2 | semidirect |
| 7. #24909511 | C2 | semidirect |
| 149. C83 | #33827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918115 | 2 |
| #24909629 | 2 |
| #24909626 | 2 |
| #24909569 | 2 |
| #24909554 | 2 |
| #24909512 | 2 |
| #24909511 | 2 |
| #24909221 | 2 |
| C83×#2216 | 2 |
| #33827 | 83 |