Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
934 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#19127504 | C2 | semidirect |
| 9. C22×Dic332 | C4 | semidirect |
| 60. Dic332 | C22⋊C4 | semidirect |
| 112. C22×C83 | #358 | semidirect |
| 135. C83 | #12732 | semidirect |
| 243. C22 | #19127504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic332 | 2 |
| C2×#19127504 | 2 |
| C2×C22⋊(C83⋊C16) | 2 |
| C83×#1808 | 2 |
| #12732 | 83 |