Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
302 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 57 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. #24909646 | C2 | semidirect |
| 3. #24909644 | C2 | semidirect |
| 4. #24908970 | C2 | semidirect |
| 5. #24905477 | C2 | semidirect |
| 6. #24905404 | C2 | semidirect |
| 7. C83×#1349 | C2 | semidirect |
| 154. #1349 | D83 | semidirect |
| 156. C83 | #12294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918897 | 2 |
| #24909646 | 2 |
| #24909644 | 2 |
| #24908970 | 2 |
| #24905477 | 2 |
| #24905404 | 2 |
| C83×#1349 | 2 |
| #12294 | 83 |