Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
206 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 88 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. #21460981 | C2 | direct (N × H) |
| 8. C2×#14519683 | C4 | semidirect |
| 9. C32×D61 | C4 | semidirect |
| 11. C2×C32×C61 | C4 | semidirect |
| 21. #14519683 | C2×C4 | semidirect |
| 23. C32×C61 | C2×C4 | semidirect |
| 64. C2×C61 | #1424 | semidirect |
| 66. D61 | #1424 | semidirect |
| 73. C2×C32 | #6923 | semidirect |
| 76. C61 | C2×#1424 | semidirect |
| 88. C32 | C2×#6923 | semidirect |
| 127. C2 | #21460981 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840688 | 2 |
| #21460981 | 2 |
| C2×C32×D61 | 2 |
| C2×#1424 | 61 |