Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
544 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 113 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. #24910380 | C2 | semidirect |
| 4. #24905859 | C2 | semidirect |
| 5. #24905365 | C2 | semidirect |
| 6. #24905321 | C2 | semidirect |
| 12. #19127908 | C4 | semidirect |
| 13. #19127898 | C4 | semidirect |
| 209. C83 | #9180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916931 | 2 |
| #24910380 | 2 |
| #24905958 | 2 |
| #24905859 | 2 |
| #24905365 | 2 |
| #24905321 | 2 |
| C83×#1517 | 2 |
| #9180 | 83 |