Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
328 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C2×#16839540 | C2 | semidirect |
| 5. #21443927 | C2 | semidirect |
| 6. #21443917 | C2 | semidirect |
| 7. C61×#1943 | C2 | semidirect |
| 15. #16839565 | C4 | semidirect |
| 16. #16839562 | C4 | semidirect |
| 147. #1943 | D61 | semidirect |
| 171. C61 | #13153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839571 | 2 |
| #21447529 | 2 |
| C2×#16839540 | 2 |
| #21446712 | 2 |
| #21443927 | 2 |
| #21443917 | 2 |
| C61×#1943 | 2 |
| #13153 | 61 |