Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
304 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 4. #24905635 | C2 | semidirect |
| 5. #24905635 | C2 | semidirect |
| 6. #24905632 | C2 | semidirect |
| 7. C83×#1411 | C2 | semidirect |
| 158. #1411 | D83 | semidirect |
| 159. C83 | #13612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918539 | 2 |
| #24909156 | 2 |
| #24909151 | 2 |
| #24905635 | 2 |
| #24905632 | 2 |
| C83×#1411 | 2 |
| #13612 | 83 |