Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
756 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 1. C2×#16839608 | C2 | semidirect |
| 2. #21445887 | C2 | semidirect |
| 4. #21443697 | C2 | semidirect |
| 16. C61×#390 | C4 | semidirect |
| 17. C61×#389 | C4 | semidirect |
| 179. #390 | Dic61 | semidirect |
| 180. #389 | Dic61 | semidirect |
| 189. C61 | #9149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839608 | 2 |
| #21445887 | 2 |
| C2×#16839496 | 2 |
| #21443697 | 2 |
| C61×#2854 | 2 |
| #9149 | 61 |