Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
190 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 115 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. #24905665 | C2 | semidirect |
| 3. #24905663 | C2 | semidirect |
| 9. C2×C32×C83 | C4 | semidirect |
| 57. C83 | #13633 | semidirect |
| 60. C2×C32 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909247 | 2 |
| #24905665 | 2 |
| #24905663 | 2 |
| C22×C32×C83 | 2 |
| #13633 | 83 |