Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
278 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 278 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 |
|---|---|---|
| 14. #16839589 | C4 | semidirect |
| 15. #16839587 | C4 | semidirect |
| 133. C61 | #13170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839591 | 2 |
| #21447601 | 2 |
| C2×#16839538 | 2 |
| #21446567 | 2 |
| #21443916 | 2 |
| #21443914 | 2 |
| C61×#1945 | 2 |
| #13170 | 61 |