Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#16840191 | C2 | semidirect |
| 2. C2×D16×D61 | C2 | semidirect |
| 3. #21448130 | C2 | direct (N × H) |
| 4. C2×#16839601 | C2 | semidirect |
| 5. C2×#16839600 | C2 | semidirect |
| 6. C2×#16839597 | C2 | semidirect |
| 7. C2×#16839595 | C2 | semidirect |
| 8. C2×C61×D32 | C2 | semidirect |
| 12. #16840191 | C22 | semidirect |
| 13. C2×Dic488 | C22 | semidirect |
| 18. D16×D61 | C22 | semidirect |
| 20. #16839601 | C22 | semidirect |
| 21. #16839600 | C22 | semidirect |
| 22. #16839597 | C22 | semidirect |
| 23. #16839595 | C22 | semidirect |
| 24. C2×#14519683 | C22 | semidirect |
| 26. C2×D16×C61 | C22 | semidirect |
| 27. C61×D32 | C22 | semidirect |
| 28. C2×C32×C61 | C22 | semidirect |
| 41. Dic488 | C23 | semidirect |
| 49. #14519683 | C23 | semidirect |
| 55. D16×C61 | C23 | semidirect |
| 57. C32×C61 | C23 | semidirect |
| 134. C2×D32 | D61 | semidirect |
| 138. C2×C61 | #2263 | semidirect |
| 153. C2×D16 | C2×D61 | semidirect |
| 158. D32 | C2×D61 | semidirect |
| 161. C2×C32 | C2×D61 | semidirect |
| 162. C61 | C2×#2263 | semidirect |
| 185. D16 | C22×D61 | semidirect |
| 191. C32 | C22×D61 | semidirect |
| 265. C2 | #21448130 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840191 | 2 |
| C2×D16×D61 | 2 |
| #21448130 | 2 |
| C2×#16839601 | 2 |
| C2×#16839600 | 2 |
| C2×#16839597 | 2 |
| C2×#16839595 | 2 |
| C2×C61×D32 | 2 |
| C2×#2263 | 61 |