Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
542 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 139 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×D16×D61 | C2 | semidirect |
| 2. C2×D1952 | C2 | semidirect |
| 3. C2×#16839597 | C2 | semidirect |
| 4. D32×D61 | C2 | direct (N × H) |
| 5. C2×C32×D61 | C2 | semidirect |
| 6. C2×C61×D32 | C2 | semidirect |
| 8. C2×D976 | C22 | semidirect |
| 11. D16×D61 | C22 | semidirect |
| 13. D1952 | C22 | semidirect |
| 14. #16839597 | C22 | semidirect |
| 15. C2×#14519683 | C22 | semidirect |
| 16. C32×D61 | C22 | semidirect |
| 17. C2×D16×C61 | C22 | semidirect |
| 18. C61×D32 | C22 | semidirect |
| 19. C2×C32×C61 | C22 | semidirect |
| 27. D976 | C23 | semidirect |
| 32. #14519683 | C23 | semidirect |
| 35. D16×C61 | C23 | semidirect |
| 37. C32×C61 | C23 | semidirect |
| 81. C2×D61 | D32 | direct (N × H) |
| 90. C2×D32 | D61 | direct (N × H) |
| 93. C2×C61 | C2×D32 | semidirect |
| 96. D61 | C2×D32 | direct (N × H) |
| 102. C2×D16 | C2×D61 | semidirect |
| 106. D32 | C2×D61 | direct (N × H) |
| 109. C2×C32 | C2×D61 | semidirect |
| 110. C61 | C22×D32 | semidirect |
| 122. D16 | C22×D61 | semidirect |
| 128. C32 | C22×D61 | semidirect |
| 179. C2 | D32×D61 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D61 | 2 |
| C2×D1952 | 2 |
| C2×#16839597 | 2 |
| D32×D61 | 2 |
| C2×C32×D61 | 2 |
| C2×C61×D32 | 2 |
| C22×D32 | 61 |