Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
270 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 2. #21460924 | C2 | semidirect |
| 3. C4×#14519827 | C2 | semidirect |
| 5. D61⋊C32 | C4 | direct (N × H) |
| 14. #14519827 | C2×C4 | semidirect |
| 49. C4×D61 | C32 | semidirect |
| 61. C4×C61 | C2×C32 | semidirect |
| 65. Dic61 | C2×C32 | semidirect |
| 72. D61 | C4×C32 | semidirect |
| 82. C61 | C2×C4×C32 | semidirect |
| 131. C4 | D61⋊C32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D61⋊C32 | 2 |
| #21460924 | 2 |
| C4×#14519827 | 2 |
| C4×C16×D61 | 2 |
| C2×C4×C32 | 61 |