Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
418 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 93 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. #24908415 | C2 | semidirect |
| 4. #24906188 | C2 | semidirect |
| 6. #24905332 | C2 | semidirect |
| 7. C83×#1285 | C2 | semidirect |
| 10. #19128110 | C4 | semidirect |
| 11. #19128061 | C4 | semidirect |
| 195. #1285 | D83 | semidirect |
| 196. C83 | #9375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918686 | 2 |
| #24916604 | 2 |
| #24908415 | 2 |
| #24906188 | 2 |
| #24905986 | 2 |
| #24905332 | 2 |
| C83×#1285 | 2 |
| #9375 | 83 |