Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1426 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1426 conjugacy classes of subgroups — too many to draw. Only its 259 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 |
|---|---|---|
| 7. C23×Q8×C61 | C4 | semidirect |
| 11. C22×C4⋊C4×C61 | C4 | semidirect |
| 12. C22×C4⋊C4×C61 | C4 | semidirect |
| 18. C2×C22⋊Dic61 | Q8 | semidirect |
| 153. C23×Q8 | Dic61 | semidirect |
| 157. C22×C4⋊C4 | Dic61 | semidirect |
| 158. C22×C4⋊C4 | Dic61 | semidirect |
| 163. C61 | #11381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839529 | 2 |
| #21444042 | 2 |
| C22×C22⋊Q8×C61 | 2 |
| #11381 | 61 |