Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1062 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 288 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. #21461747 | C2 | semidirect |
| 2. #21461746 | C2 | semidirect |
| 51. C42×C61 | M16 | semidirect |
| 58. C4×Dic61 | M16 | semidirect |
| 112. C61 | #20772 | semidirect |
| 156. C42 | #11758213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461747 | 2 |
| #21461746 | 2 |
| #21461483 | 2 |
| C43×D61 | 2 |
| #20772 | 61 |