Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
396 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. #21457171 | C2 | semidirect |
| 2. #21447748 | C2 | semidirect |
| 4. #21443830 | C2 | semidirect |
| 5. #21443827 | C2 | semidirect |
| 6. #21443759 | C2 | semidirect |
| 7. C61×#2054 | C2 | semidirect |
| 177. #2054 | D61 | semidirect |
| 207. C61 | #12160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457171 | 2 |
| #21447748 | 2 |
| #21447731 | 2 |
| #21443830 | 2 |
| #21443827 | 2 |
| #21443759 | 2 |
| C61×#2054 | 2 |
| #12160 | 61 |