Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
364 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 108 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. #21460765 | C2 | semidirect |
| 120. C61 | #11456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840658 | 2 |
| #21460765 | 2 |
| #21454383 | 2 |
| #11456 | 61 |