Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
460 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 12. C2×#14519723 | C4 | semidirect |
| 180. C61 | #13020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519723 | 2 |
| #21454687 | 2 |
| #21447540 | 2 |
| #21446732 | 2 |
| #21443916 | 2 |
| #21443909 | 2 |
| C2×C61×#362 | 2 |
| #13020 | 61 |