Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
306 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 79 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. #24909264 | C2 | semidirect |
| 3. #24906208 | C2 | semidirect |
| 4. #24905434 | C2 | semidirect |
| 5. #24905432 | C2 | semidirect |
| 6. #24905430 | C2 | semidirect |
| 7. C83×#1333 | C2 | semidirect |
| 156. #1333 | D83 | semidirect |
| 157. C83 | #11656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918031 | 2 |
| #24909264 | 2 |
| #24906208 | 2 |
| #24905434 | 2 |
| #24905432 | 2 |
| #24905430 | 2 |
| C83×#1333 | 2 |
| #11656 | 83 |