Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
338 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 4. #21445992 | C2 | semidirect |
| 5. #21443917 | C2 | semidirect |
| 6. #21443902 | C2 | semidirect |
| 7. C61×#1383 | C2 | semidirect |
| 136. #1383 | D61 | semidirect |
| 156. C61 | #13487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839576 | 2 |
| C2×#16839574 | 2 |
| #21446693 | 2 |
| #21445992 | 2 |
| #21443917 | 2 |
| #21443902 | 2 |
| C61×#1383 | 2 |
| #13487 | 61 |