Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
214 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 97 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×C32×D61 | C2 | semidirect |
| 3. #21443956 | C2 | semidirect |
| 4. C4×#14519683 | C2 | semidirect |
| 5. C61×C4⋊C32 | C2 | semidirect |
| 23. #14519683 | D4 | semidirect |
| 47. D244 | C32 | semidirect |
| 58. C2×D61 | C2×C32 | semidirect |
| 60. C4×C61 | C2×C32 | semidirect |
| 66. C4⋊C32 | D61 | semidirect |
| 82. C61 | D4×C32 | semidirect |
| 128. C4 | C32×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D61 | 2 |
| C16×D244 | 2 |
| #21443956 | 2 |
| C4×#14519683 | 2 |
| C61×C4⋊C32 | 2 |
| D4×C32 | 61 |