Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
542 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 542 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. #24916486 | C2 | semidirect |
| 3. #24907474 | C2 | semidirect |
| 4. #24906024 | C2 | semidirect |
| 5. #24905861 | C2 | semidirect |
| 6. #24905323 | C2 | semidirect |
| 7. C83×#1301 | C2 | semidirect |
| 12. #19127907 | C4 | semidirect |
| 13. #19127897 | C4 | semidirect |
| 200. #1301 | D83 | semidirect |
| 202. C83 | #9305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916929 | 2 |
| #24916486 | 2 |
| #24907474 | 2 |
| #24906024 | 2 |
| #24905861 | 2 |
| #24905323 | 2 |
| C83×#1301 | 2 |
| #9305 | 83 |