Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1810 conjugacy classes of subgroups; only the 319 normal subgroups are shown.
This group has 1810 conjugacy classes of subgroups — too many to draw. Only its 319 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. #24905725 | C2 | semidirect |
| 2. #24905712 | C2 | semidirect |
| 3. #24905704 | C2 | semidirect |
| 4. #24905700 | C2 | semidirect |
| 15. #392×C83 | C4 | semidirect |
| 160. C83 | #14651 | semidirect |
| 167. #392 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24905725 | 2 |
| #24905712 | 2 |
| #24905704 | 2 |
| #24905700 | 2 |
| C2×#392×C83 | 2 |
| #14651 | 83 |