Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
314 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 314 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. #21458424 | C2 | semidirect |
| 2. #21448060 | C2 | semidirect |
| 3. #21447851 | C2 | semidirect |
| 4. #21443872 | C2 | semidirect |
| 5. #21443785 | C2 | semidirect |
| 6. #21443777 | C2 | semidirect |
| 7. C61×#1687 | C2 | semidirect |
| 150. #1687 | D61 | semidirect |
| 179. C61 | #12348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458424 | 2 |
| #21448060 | 2 |
| #21447851 | 2 |
| #21443872 | 2 |
| #21443785 | 2 |
| #21443777 | 2 |
| C61×#1687 | 2 |
| #12348 | 61 |