Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
344 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 59 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. #21447769 | C2 | semidirect |
| 3. #21447125 | C2 | semidirect |
| 4. #21443807 | C2 | semidirect |
| 5. #21443804 | C2 | semidirect |
| 6. #21443772 | C2 | semidirect |
| 7. C61×#3263 | C2 | semidirect |
| 167. #3263 | D61 | semidirect |
| 198. C61 | #12172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447769 | 2 |
| #21447764 | 2 |
| #21447125 | 2 |
| #21443807 | 2 |
| #21443804 | 2 |
| #21443772 | 2 |
| C61×#3263 | 2 |
| #12172 | 61 |