Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
594 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. C2×#19128079 | C2 | semidirect |
| 4. C2×#19127504 | C2 | semidirect |
| 6. #24905540 | C2 | semidirect |
| 7. C2×#358×C83 | C2 | semidirect |
| 154. C2×Dic83 | SD32 | semidirect |
| 197. C2×#358 | D83 | semidirect |
| 200. C83 | #13327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581737 | 2 |
| C22×#14581735 | 2 |
| C2×#19128079 | 2 |
| C2×#19127504 | 2 |
| #24908327 | 2 |
| #24905540 | 2 |
| C2×#358×C83 | 2 |
| #13327 | 83 |