Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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. C22×Dic482 | C2 | semidirect |
| 2. #21440672 | C2 | direct (N × H) |
| 3. C2×#16838760 | C2 | semidirect |
| 4. C2×#16838758 | C2 | semidirect |
| 5. C2×#16838754 | C2 | semidirect |
| 10. C2×Dic482 | C22 | semidirect |
| 12. #16838760 | C22 | semidirect |
| 13. #16838758 | C22 | semidirect |
| 14. #16838754 | C22 | semidirect |
| 54. C2×C241 | #137 | semidirect |
| 56. C241 | C2×#137 | semidirect |
| 111. C2 | #21440672 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic482 | 2 |
| #21440672 | 2 |
| C2×#16838760 | 2 |
| C2×#16838758 | 2 |
| C2×#16838754 | 2 |
| C2×#41×C241 | 2 |
| C2×#137 | 241 |