Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
406 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24906077 | C2 | semidirect |
| 4. #24905885 | C2 | semidirect |
| 5. #24905362 | C2 | semidirect |
| 6. #24905335 | C2 | semidirect |
| 189. C83 | #9314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917625 | 2 |
| #24906077 | 2 |
| #24905897 | 2 |
| #24905885 | 2 |
| #24905362 | 2 |
| #24905335 | 2 |
| C83×#2923 | 2 |
| #9314 | 83 |