Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21446764 | C2 | semidirect |
| 5. #21443712 | C2 | semidirect |
| 6. #21443674 | C2 | semidirect |
| 7. C61×#1506 | C2 | semidirect |
| 10. #16840039 | C4 | semidirect |
| 11. #16839964 | C4 | semidirect |
| 179. #1506 | D61 | semidirect |
| 210. C61 | #9327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455914 | 2 |
| #21448463 | 2 |
| #21446764 | 2 |
| #21444261 | 2 |
| #21443712 | 2 |
| #21443674 | 2 |
| C61×#1506 | 2 |
| #9327 | 61 |