Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
386 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. C2×#16839591 | C2 | semidirect |
| 3. #21447569 | C2 | semidirect |
| 4. C2×#16839568 | C2 | semidirect |
| 5. C2×#16839547 | C2 | semidirect |
| 6. #21445866 | C2 | semidirect |
| 7. C61×#1385 | C2 | semidirect |
| 175. #1385 | D61 | semidirect |
| 201. C61 | #13392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455540 | 2 |
| C2×#16839591 | 2 |
| #21447569 | 2 |
| C2×#16839568 | 2 |
| C2×#16839547 | 2 |
| #21445866 | 2 |
| C61×#1385 | 2 |
| #13392 | 61 |