Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
472 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 91 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. #24916480 | C2 | semidirect |
| 3. #24907274 | C2 | semidirect |
| 4. #24906055 | C2 | semidirect |
| 5. #24905356 | C2 | semidirect |
| 6. #24905336 | C2 | semidirect |
| 7. C83×#1505 | C2 | semidirect |
| 10. #19127983 | C4 | semidirect |
| 11. #19127978 | C4 | semidirect |
| 12. #19127898 | C4 | semidirect |
| 13. #19127893 | C4 | semidirect |
| 207. #1505 | D83 | semidirect |
| 210. C83 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917608 | 2 |
| #24916480 | 2 |
| #24907274 | 2 |
| #24906055 | 2 |
| #24905356 | 2 |
| #24905336 | 2 |
| C83×#1505 | 2 |
| #9162 | 83 |