Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
454 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #24908308 | C2 | semidirect |
| 5. C83⋊#1309 | C2 | semidirect |
| 6. #24905354 | C2 | semidirect |
| 7. C83×#1549 | C2 | semidirect |
| 151. Dic166 | #101 | semidirect |
| 187. #1549 | D83 | semidirect |
| 191. C83 | #9358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917272 | 2 |
| #24916592 | 2 |
| #24908308 | 2 |
| #24905900 | 2 |
| C83⋊#1309 | 2 |
| #24905354 | 2 |
| C83×#1549 | 2 |
| #9358 | 83 |