Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
324 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 3. C2×#16839537 | C2 | semidirect |
| 5. #21446565 | C2 | semidirect |
| 6. #21443916 | C2 | semidirect |
| 7. C61×#1381 | C2 | semidirect |
| 16. #16839567 | C4 | semidirect |
| 17. #16839564 | C4 | semidirect |
| 139. #1381 | D61 | semidirect |
| 160. C61 | #13152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839568 | 2 |
| #21447527 | 2 |
| C2×#16839537 | 2 |
| #21446705 | 2 |
| #21446565 | 2 |
| #21443916 | 2 |
| C61×#1381 | 2 |
| #13152 | 61 |