Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
454 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 135 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×#16839582 | C2 | semidirect |
| 4. #21443901 | C2 | semidirect |
| 5. C61×#1376 | C2 | semidirect |
| 128. #1376 | D61 | semidirect |
| 146. C61 | #12789 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839716 | 2 |
| C2×#16839582 | 2 |
| #21447429 | 2 |
| #21443901 | 2 |
| C61×#1376 | 2 |
| #12789 | 61 |