Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
214 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 56 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. D16×#6923 | C2 | semidirect |
| 2. #21460980 | C2 | semidirect |
| 3. #21460968 | C2 | semidirect |
| 4. C32×#6923 | C2 | semidirect |
| 12. D1952 | C4 | semidirect |
| 13. #16839597 | C4 | semidirect |
| 15. C61×D32 | C4 | semidirect |
| 23. D976 | C2×C4 | semidirect |
| 26. #14519683 | C2×C4 | semidirect |
| 27. D16×C61 | C2×C4 | semidirect |
| 28. C32×C61 | C2×C4 | semidirect |
| 62. #6923 | D32 | direct (N × H) |
| 79. D32 | #6923 | direct (N × H) |
| 85. C61 | C4×D32 | semidirect |
| 90. D16 | C2×#6923 | semidirect |
| 98. C32 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D16×#6923 | 2 |
| #21460980 | 2 |
| #21460968 | 2 |
| C32×#6923 | 2 |
| D32×D61 | 2 |
| C4×D32 | 61 |