Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 452 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 |
|---|---|---|
| 2. #21447493 | C2 | semidirect |
| 4. #21447472 | C2 | semidirect |
| 6. #21445619 | C2 | semidirect |
| 7. C61×#1812 | C2 | semidirect |
| 8. C22×#11758190 | C4 | semidirect |
| 15. #16839800 | C4 | semidirect |
| 16. #16839772 | C4 | semidirect |
| 17. #16839768 | C4 | semidirect |
| 212. #1812 | D61 | semidirect |
| 243. C61 | #13229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455458 | 2 |
| #21447493 | 2 |
| #21447490 | 2 |
| #21447472 | 2 |
| #21447468 | 2 |
| #21445619 | 2 |
| C61×#1812 | 2 |
| #13229 | 61 |