Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
526 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 97 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. #24908437 | C2 | semidirect |
| 4. C2×#19127443 | C2 | semidirect |
| 6. #24905345 | C2 | semidirect |
| 7. C2×#491×C83 | C2 | semidirect |
| 189. C2×#491 | D83 | semidirect |
| 196. C83 | #10083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128063 | 2 |
| #24915513 | 2 |
| #24908437 | 2 |
| C2×#19127443 | 2 |
| C2×#19127440 | 2 |
| #24905345 | 2 |
| C2×#491×C83 | 2 |
| #10083 | 83 |