Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
484 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 1. #24915735 | C2 | semidirect |
| 3. #24905345 | C2 | semidirect |
| 4. #24905344 | C2 | semidirect |
| 39. #127×C83 | Q8 | semidirect |
| 148. C83 | #10358 | semidirect |
| 169. #127 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24915735 | 2 |
| #24908288 | 2 |
| #24905345 | 2 |
| #24905344 | 2 |
| C83×#1961 | 2 |
| #10358 | 83 |