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. #24908416 | C2 | semidirect |
| 5. #24905332 | C2 | semidirect |
| 6. #24905320 | C2 | semidirect |
| 7. C83×#1558 | C2 | semidirect |
| 9. #19128107 | C4 | semidirect |
| 10. #19128063 | C4 | semidirect |
| 192. #1558 | 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 |
|---|---|
| #24918684 | 2 |
| #24916604 | 2 |
| #24908416 | 2 |
| #24905989 | 2 |
| #24905332 | 2 |
| #24905320 | 2 |
| C83×#1558 | 2 |
| #9375 | 83 |