Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. #24918122 | C2 | semidirect |
| 3. #24909683 | C2 | semidirect |
| 4. #24909640 | C2 | semidirect |
| 5. #24909545 | C2 | semidirect |
| 7. #24909356 | C2 | semidirect |
| 8. C83×#2166 | C2 | semidirect |
| 13. #19128103 | C22 | semidirect |
| 14. #19128081 | C22 | semidirect |
| 22. #19127809 | C22 | semidirect |
| 26. #19127524 | C22 | semidirect |
| 27. #19127518 | C22 | semidirect |
| 30. #364×C83 | C22 | semidirect |
| 32. #347×C83 | C22 | semidirect |
| 168. #2166 | D83 | semidirect |
| 169. C83 | #33693 | semidirect |
| 189. #364 | C2×D83 | semidirect |
| 193. #347 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918122 | 2 |
| #24916367 | 2 |
| #24909683 | 2 |
| #24909640 | 2 |
| #24909545 | 2 |
| #24909416 | 2 |
| #24909356 | 2 |
| C83×#2166 | 2 |
| #33693 | 83 |