Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #24906013 | C2 | semidirect |
| 5. #24905885 | C2 | semidirect |
| 6. #24905324 | C2 | semidirect |
| 7. C83×#1288 | C2 | semidirect |
| 10. #19128110 | C4 | semidirect |
| 11. #19128110 | C4 | semidirect |
| 12. #19128061 | C4 | semidirect |
| 13. #19128061 | C4 | semidirect |
| 195. #1288 | D83 | semidirect |
| 197. C83 | #9369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918705 | 2 |
| #24916448 | 2 |
| #24906038 | 2 |
| #24906013 | 2 |
| #24905885 | 2 |
| #24905324 | 2 |
| C83×#1288 | 2 |
| #9369 | 83 |