Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
378 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 91 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. #24909229 | C2 | semidirect |
| 4. #24909183 | C2 | semidirect |
| 6. #24905577 | C2 | semidirect |
| 7. C83×#1979 | C2 | semidirect |
| 167. #1979 | D83 | semidirect |
| 170. C83 | #13443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128142 | 2 |
| #24909229 | 2 |
| #24909210 | 2 |
| #24909183 | 2 |
| #24908361 | 2 |
| #24905577 | 2 |
| C83×#1979 | 2 |
| #13443 | 83 |