Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 99 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×#16839577 | C2 | semidirect |
| 4. #21447538 | C2 | semidirect |
| 6. #21443901 | C2 | semidirect |
| 7. C61×#1945 | C2 | semidirect |
| 160. #1945 | D61 | semidirect |
| 184. C61 | #13414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840146 | 2 |
| C2×#16839577 | 2 |
| C2×#16839574 | 2 |
| #21447538 | 2 |
| #21447534 | 2 |
| #21443901 | 2 |
| C61×#1945 | 2 |
| #13414 | 61 |