Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
930 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 159 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. #24909199 | C2 | semidirect |
| 2. #24909179 | C2 | semidirect |
| 3. #24909084 | C2 | semidirect |
| 4. #24907509 | C2 | semidirect |
| 6. C2×#14581732 | C22 | semidirect |
| 7. #19127739 | C22 | semidirect |
| 18. C2×#135×C83 | C4 | semidirect |
| 20. C22×D8×C83 | C4 | semidirect |
| 180. C83 | #12741 | semidirect |
| 186. C2×#135 | Dic83 | semidirect |
| 188. C22×D8 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909199 | 2 |
| #24909179 | 2 |
| #24909084 | 2 |
| #24907509 | 2 |
| C2×#576×C83 | 2 |
| #12741 | 83 |