Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24905976 | C2 | semidirect |
| 5. #24905935 | C2 | semidirect |
| 6. #24905291 | C2 | semidirect |
| 7. C83×#1287 | C2 | semidirect |
| 10. #19128106 | C4 | semidirect |
| 11. #19128099 | C4 | semidirect |
| 12. #19128048 | C4 | semidirect |
| 13. #19128048 | C4 | semidirect |
| 174. #1287 | D83 | semidirect |
| 176. C83 | #9279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918601 | 2 |
| #24916541 | 2 |
| #24905976 | 2 |
| #24905972 | 2 |
| #24905935 | 2 |
| #24905291 | 2 |
| C83×#1287 | 2 |
| #9279 | 83 |