Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
432 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 432 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. #349×D83 | C2 | semidirect |
| 3. #338×D83 | C2 | semidirect |
| 4. #24905458 | C2 | semidirect |
| 5. #24905456 | C2 | semidirect |
| 6. #24905454 | C2 | semidirect |
| 7. C83×#1341 | C2 | semidirect |
| 208. #1341 | D83 | semidirect |
| 209. C83 | #11688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917070 | 2 |
| #349×D83 | 2 |
| #338×D83 | 2 |
| #24905458 | 2 |
| #24905456 | 2 |
| #24905454 | 2 |
| C83×#1341 | 2 |
| #11688 | 83 |