Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
328 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 95 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×#16839539 | C2 | semidirect |
| 5. #21446555 | C2 | semidirect |
| 6. #21443929 | C2 | semidirect |
| 7. C61×#1383 | C2 | semidirect |
| 16. #16839567 | C4 | semidirect |
| 17. #16839564 | C4 | semidirect |
| 149. #1383 | 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 |
| #21447532 | 2 |
| C2×#16839539 | 2 |
| #21446710 | 2 |
| #21446555 | 2 |
| #21443929 | 2 |
| C61×#1383 | 2 |
| #13153 | 61 |