Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
930 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 135 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. #24909198 | C2 | semidirect |
| 3. #24909178 | C2 | semidirect |
| 4. #24909084 | C2 | semidirect |
| 5. C83×#1812 | C2 | semidirect |
| 11. C2×#14581814 | C4 | semidirect |
| 13. C22×D664 | C4 | semidirect |
| 15. C2×#14581732 | C22 | semidirect |
| 20. #427×C83 | C22 | semidirect |
| 179. #1812 | D83 | semidirect |
| 180. C83 | #12741 | semidirect |
| 192. #427 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128506 | 2 |
| #24909198 | 2 |
| #24909178 | 2 |
| #24909084 | 2 |
| C83×#1812 | 2 |
| #12741 | 83 |