Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
316 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 22. #14519717 | Q8 | semidirect |
| 120. C61 | #13270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447585 | 2 |
| #21447424 | 2 |
| #21443905 | 2 |
| #21443901 | 2 |
| C61×#2960 | 2 |
| #13270 | 61 |