Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
256 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 63 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. #24909607 | C2 | semidirect |
| 3. #24907056 | C2 | semidirect |
| 4. #24906257 | C2 | semidirect |
| 5. #24905526 | C2 | semidirect |
| 6. #24905508 | C2 | semidirect |
| 7. C83×#1365 | C2 | semidirect |
| 55. D664 | SD16 | semidirect |
| 120. #1365 | D83 | semidirect |
| 122. C83 | #12418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909607 | 2 |
| #24909499 | 2 |
| #24907056 | 2 |
| #24906257 | 2 |
| #24905526 | 2 |
| #24905508 | 2 |
| C83×#1365 | 2 |
| #12418 | 83 |