Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
324 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#19127476 | C2 | semidirect |
| 4. #24908212 | C2 | semidirect |
| 5. #24905558 | C2 | semidirect |
| 6. #24905557 | C2 | semidirect |
| 21. #358×C83 | C4 | semidirect |
| 22. #357×C83 | C4 | semidirect |
| 145. C83 | #13152 | semidirect |
| 157. #358 | Dic83 | semidirect |
| 158. #357 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127508 | 2 |
| C2×#19127476 | 2 |
| #24908352 | 2 |
| #24908212 | 2 |
| #24905558 | 2 |
| #24905557 | 2 |
| C83×#2138 | 2 |
| #13152 | 83 |