Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
680 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 171 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. #24916331 | C2 | semidirect |
| 4. #24909527 | C2 | semidirect |
| 5. #24909511 | C2 | semidirect |
| 6. #24909221 | C2 | semidirect |
| 7. #24909183 | C2 | semidirect |
| 9. C22×Q32×C83 | C2 | semidirect |
| 173. C22×Q32 | D83 | semidirect |
| 181. C83 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128142 | 2 |
| #24917952 | 2 |
| #24916331 | 2 |
| #24909527 | 2 |
| #24909511 | 2 |
| #24909221 | 2 |
| #24909183 | 2 |
| #24909171 | 2 |
| C22×Q32×C83 | 2 |
| #33588 | 83 |