Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
396 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 85 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. #24909261 | C2 | semidirect |
| 3. #24906225 | C2 | semidirect |
| 4. #24905512 | C2 | semidirect |
| 5. #24905510 | C2 | semidirect |
| 6. #24905508 | C2 | semidirect |
| 7. C83×#1362 | C2 | semidirect |
| 149. #1362 | D83 | semidirect |
| 152. C83 | #11963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917892 | 2 |
| #24909261 | 2 |
| #24906225 | 2 |
| #24905512 | 2 |
| #24905510 | 2 |
| #24905508 | 2 |
| C83×#1362 | 2 |
| #11963 | 83 |