Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
314 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #24909706 | C2 | semidirect |
| 2. #24909498 | C2 | semidirect |
| 3. #24906942 | C2 | semidirect |
| 4. #24905515 | C2 | semidirect |
| 5. #24905430 | C2 | semidirect |
| 6. #24905421 | C2 | semidirect |
| 7. C83×#3355 | C2 | semidirect |
| 153. #3355 | D83 | semidirect |
| 160. C83 | #12348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909706 | 2 |
| #24909498 | 2 |
| #24906942 | 2 |
| #24905515 | 2 |
| #24905430 | 2 |
| #24905421 | 2 |
| C83×#3355 | 2 |
| #12348 | 83 |