Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 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. #24909343 | C2 | semidirect |
| 3. #24905646 | C2 | semidirect |
| 4. #24905596 | C2 | semidirect |
| 5. C83×#1425 | C2 | semidirect |
| 8. Dic1328 | C4 | semidirect |
| 9. #19127540 | C4 | semidirect |
| 10. D2656 | C4 | semidirect |
| 64. #1425 | D83 | semidirect |
| 67. C83 | #13656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909772 | 2 |
| #24909343 | 2 |
| #24905646 | 2 |
| #24905596 | 2 |
| C83×#1425 | 2 |
| #13656 | 83 |