Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1128 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 351 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. #24916058 | C2 | semidirect |
| 3. #24909200 | C2 | semidirect |
| 4. C2×#19127512 | C2 | semidirect |
| 5. C83×#3407 | C2 | semidirect |
| 7. #19128518 | C4 | semidirect |
| 9. #19128506 | C4 | semidirect |
| 14. #19127739 | C22 | semidirect |
| 15. C2×#14581724 | C22 | semidirect |
| 16. #19127512 | C22 | semidirect |
| 17. #19127512 | C22 | semidirect |
| 20. C2×M32×C83 | C22 | semidirect |
| 31. #14581814 | C2×C4 | semidirect |
| 33. C2×Dic332 | C2×C4 | semidirect |
| 35. C2×D664 | C2×C4 | semidirect |
| 127. #3407 | D83 | semidirect |
| 131. C83 | #33388 | semidirect |
| 141. C2×M32 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24922237 | 2 |
| #24916058 | 2 |
| #24909200 | 2 |
| C2×#19127512 | 2 |
| C83×#3407 | 2 |
| #33388 | 83 |