Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1770 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1770 conjugacy classes of subgroups — too many to draw. Only its 451 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. C2×#16839630 | C2 | semidirect |
| 4. #21444052 | C2 | semidirect |
| 5. C2×C43×C61 | C2 | semidirect |
| 8. C2×#14519771 | C4 | semidirect |
| 58. C42×C61 | C22⋊C4 | semidirect |
| 78. C2×C4×C61 | #126 | semidirect |
| 103. C2×C43 | D61 | semidirect |
| 123. C61 | #14711 | semidirect |
| 167. C42 | #11758198 | semidirect |
| 191. C2×C4 | #14519771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519771 | 2 |
| C2×#16839630 | 2 |
| #21444057 | 2 |
| #21444052 | 2 |
| C2×C43×C61 | 2 |
| #14711 | 61 |