Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
520 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#19127517 | C2 | semidirect |
| 4. #24909183 | C2 | semidirect |
| 6. #24905559 | C2 | semidirect |
| 7. C22×Q32×C83 | C2 | semidirect |
| 189. C22×Q32 | D83 | semidirect |
| 196. C83 | #13322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127973 | 2 |
| #24917114 | 2 |
| C2×#19127517 | 2 |
| #24909183 | 2 |
| C2×#19127484 | 2 |
| #24905559 | 2 |
| C22×Q32×C83 | 2 |
| #13322 | 83 |