Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#19127739 | C2 | semidirect |
| 3. #24909672 | C2 | semidirect |
| 4. #24909655 | C2 | semidirect |
| 5. #24909251 | C2 | semidirect |
| 6. #24909176 | C2 | semidirect |
| 7. C83×#2112 | C2 | semidirect |
| 20. #19127529 | C22 | semidirect |
| 21. #19127527 | C22 | semidirect |
| 22. #19127506 | C22 | semidirect |
| 23. #19127503 | C22 | semidirect |
| 150. #2112 | D83 | semidirect |
| 151. C83 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917044 | 2 |
| C2×#19127739 | 2 |
| #24909672 | 2 |
| #24909655 | 2 |
| #24909251 | 2 |
| #24909176 | 2 |
| C83×#2112 | 2 |
| #33647 | 83 |