Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
298 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 61 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. #24909709 | C2 | semidirect |
| 3. #24909508 | C2 | semidirect |
| 4. #24906953 | C2 | semidirect |
| 5. #24905516 | C2 | semidirect |
| 6. #24905422 | C2 | semidirect |
| 7. C83×#1333 | C2 | semidirect |
| 151. #1333 | D83 | semidirect |
| 153. C83 | #12350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920070 | 2 |
| #24909709 | 2 |
| #24909508 | 2 |
| #24906953 | 2 |
| #24905516 | 2 |
| #24905422 | 2 |
| C83×#1333 | 2 |
| #12350 | 83 |