Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
336 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #24905633 | C2 | semidirect |
| 4. #24905627 | C2 | semidirect |
| 6. #19128313 | C4 | semidirect |
| 7. #19128096 | C4 | semidirect |
| 10. #19128055 | C4 | semidirect |
| 15. #19127762 | C4 | semidirect |
| 27. #14581792 | C2×C4 | semidirect |
| 29. #14581784 | C2×C4 | semidirect |
| 42. #14581703 | C2×C4 | semidirect |
| 43. C4×C83⋊C8 | C2×C4 | semidirect |
| 159. C83 | #13610 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918535 | 2 |
| #24909135 | 2 |
| #24905633 | 2 |
| #24905627 | 2 |
| C83×#2127 | 2 |
| #13610 | 83 |